There is no indication that The Two Sisters has any connection with Irish mythology.
It has not been recorded in Ireland, the nearest being the version from Mrs Cecilia Costello of Birmingham, England, who was originally from Galway.
Some of the motifs of the ballad, mainly that of a murder being solved using part of the body of the victim, is a universal one.
Below - all you ever wanted to know about the Two Sisters, but were afraid to ask - from Tristam P Coffin's 'The British Traditional Ballad in North America.
Jim Carroll

10. THE TWA SISTERS
Texts: Adventure, 9-10-'23, 191 / Barry, Brit Bids Me, 40 / Beard, Personal Fsg Coll Lunsford, 43 / Belden, Mo Fsgs, 16 / Botkin, Am Play-Party Sg, 59, 337 / Brewster, Bids Sgs Ind, 42 / Bronson, I, 143 / Brown, NC Flklre, II, 32 / BFSSNE, VI, 5; IX, 4; X, 10; XI, 16; XII, 10 / Bull Tenn FLS, IV, #3, 74; VIII, #3, 71 / Chappell, Fsgs Rnke Alb, 13 / Chase, Sgs All Times, 20 / Child, I, 137; II, 508 / Child Ms., XXI, 10 / Christian Science Monitor, 12-2-'37 / Cox, Fsgs South, 20 / Cox, Trd Bid W Va, 6 / Cox, W Va School Journal and Educator, XLIV, 428, 441 / Davis, Fsgs Va, 6 / Davis, More Trd Bids Va, 35 / Davis, Trd Bid Va, 93 / Eddy, Bids Sgs Ohio, 17 / Flanders, Ancient Bids, I, 150 / Flanders, Bids Migrant NE, 209 / Flanders, New Gn Mt Sgstr, 3 / Folkways Monthly, May '62, 19 / Garrison, Searcy Cnty, 19 / Gray, Sgs Bids Me Lmbrjks, 75 / Gardner and Chickering, Bids Sgs So Mich, 32 / Greenleaf and Mansfield, Bids Sea Sgs Newfdld, 9 / Haun, Cocke Cnty, 106 / Henry, Fsgs So Hghlds, 39 / Hubbard, Bids Sgs Utah, 5 / Hudson, Fsgs Miss, 68 / Hudson, Ftunes Miss, 25 / Hudson, Spec Miss Flklre, #3 / Hummel, Oz Fsgs / JAF, 1905, 130; 1906, 233; 1917, 287; 1929, 238; 1931, 295; 1932, 1; 1935, 306; 1951, 347; 1957, 249 / Ky Folklore Record, 1958, 116 / Kincaid, Fav Mt Bids, 22 / A. Lomax, Fsgs No Am, 184 / Morris, Fsgs Fla, 243 / Neal, Brown Cnty, 60 / N.Y. Times Mgz, 10—9—'27 / Niles, More Sgs Hill-Flk, 8 / Niles, Anglo-Am Bid Stdy Bk, 36 / Perry, Carter Cnty, 98 / Pound, Am Bids Sgs, 11 / Pound, Nebr Syllabus, 11 / PTFS, X, 141 / Raine, Land Sddle Bags, 118 / Randolph, Oz Fsgs, I, 50 / Randolph, Oz Mt Flk, 211 / Richardson, Am Mt Sgs, 27 / Scarborough, Sgctchr So Mts, 164 / SharpC, Eng Fsgs So Aplchns, #4 / SharpK, Eng Fsgs So Aplchns, I, 26 / Smith and Rufty, Am Anth Old Wrld Bids, 2 I SFL, 1944, 138 / Stout, Flklre la, 1 / Thomas, Blue Ridge Cntry, 152 / Thomas, Devil's Ditties, 70 / Thomas, Sngin Gathrn, 76 / Thompson, Bdy Bts Brtchs, 393 / Va FLS Bull #s 2—8, 12 / Vincent, Lmbrjk Sgs, 27.
Local Titles: All Bow Down, Bow Ye Down, The Fair Sisters. I'll Be True to My Love, Lord of the Old Country, The Miller and the Mayor's Daughter, The Miller's Two Daughters, The Old Farmer in the Countree, The Old Lord by the Northern Sea, The Old Man of (in) the North (Old) Countree, Sister Kate, The Swim Sworn Bonny, There Was an Old Farmer (Joyner), There Was an Old Man Lived in a Gum Tree, (There Was an) Old Woman (Who) Lived on the Seashore (in the West), The Two (Three) (Little) Sisters, The Two Young Daughters, West Countree, The Youngest Daughter.
Story Types: A: A girl, jealous mat a gentleman has courted her younger sister, invites the latter on a walk and pushes her in the water to drown. A miller robs the struggling girl, rather than rescuing her, and is punished by death for his crime. Capital punishment for the elder girl may or may not be mentioned. Examples: Barry (A); Belden (C); Davis, Trd Bid Va, (A); SharpK (B).
B: Two princesses are playing by the water. The elder pushes the younger in. A miller finds the dead girl and makes a musical instrument from her body. The instrument reveals the murderer.
Examples:   Barry (E), SharpK   (K).
C: The usual story is started, but the musical instrument is made from the younger sister's body by the elder sister, and the instrument then names the murderer. This version has three-quarters of each stanza as refrain. Examples: JAF, 1932, 7.
D: A combination of Types A and B is sometimes found in which the instrument is made from the body, and both the miller and the elder girl are executed. Examples: SharpK (A).
E: The usual story is started, but the drowned girl appears to make a harp of herself and reveal her murderer.
Examples: Henry, Fsgs So Hghlds (C).
F: The usual story is told, but the miller is left out. The girl in the water may plead with her sister to pull her from the "sea-sand" (quicksand?) and be refused.        Examples: Brewster (B, C), Neal.
G: An amazing version found in Newfoundland tells of the younger sister's shoving the elder sister in the water, although the younger has received more attention from the suitor. The body is fished out with a fishing pan, the face covered with lace and the hair full of golden lumps. A ghost tells the lover how his sweetheart was killed.
Examples:   Greenleaf-Mansfield
H: The usual story is told, except the elder sister bribes the miller to push the girl back into the water. Both the sister and the miller (sometimes only the miller) are hung.
Examples: Randolph, Oz Fsgs (D); Lomax, Fsgs No Am, 184.
I: The story is like that of Type A, except the miller is the father of the two girls and pushes his own daughter into the water. Examples: Cox, Fsgs South (A).
J: The usual story is told, but the miller is the lover of the girls and seems to rescue the younger one after she has been pushed in. Examples: JAF, 1905, 131.
K: A story similar to Type J is told, but after the rescue all go to church and "now they're (which two is not clear) married I suppose".
Examples: Thompson.
L: The story is like that of Type J, except that a prince courts the girls. The miller rescues the elder sister. She falls in love with him, and they marry.
Examples: Haun.
M: The usual story is told. However, the "fisherman", who has no previous connection with the girls, seems to rescue the drowning maid. Examples:   Cox, Trd Bids W Va   (B); Perry.
N: Two little girls float down a stream in a boat. Charles Miller comes out with his hook and pulls one out by the hair and makes a fiddle of her body. Examples: BFSSNE, XII, 10 .
O: The story is like that of Type L, except the miller rescues the younger sister after she promises to marry him. The tone is comic.
Examples: Brown (A).
P: The story is similar to Type A, except the sisters (it is not clear whether this includes the one pushed back in the water), flee "beyond the seas and died old maids among black savagees".
Examples: Flanders, Ancient Bids (C).
Q: The usual opening of the Type A story is followed. However, the miller's son sees the younger sister's body in the dam. The miller drains the dam and removes the body of the girl. A passing harper makes an instrument of the bones and the murder is revealed as he plays and sings.
Examples: Davis, More Trd Bids Va (AA).
Discussion: This song and the similar tale (see Aarne-Thompson, Mt. 780) still have current traditions in Europe. The ballad is also current in Britain (Child, I, 118) and has more American story variations than any other song. Thus, it makes an excellent subject for study. Paul Brewster has done a very complete survey of both the song and the tale in FFC, #147 (1953) and included a useful bibliography to both in Bids Sgs lnd, 42-43. He feels the song began in Norway before 1600, spread through Scandinavia, and then to Britain and the West. However, he thinks the tale is of Slavic origin. This thesis (see also his article The Geographical Distribution of "The Twa Sisters" in Annuario de la Sociedad Folklorica de Mexico, 1944, 49-54), along with Harbison Parker's "The Twa Sisters"—Going Which Way? in JAF, 1951, 347-360), re-evaluates Knut Leist0l's belief that the ballad was first composed in Britain, split into two versions, both of which came to Scandinavia, one to Norway and one to Denmark. Parker believes the ballad to have originated in Western Scandinavia, and the British versions to stem from Faroe or Norwegian texts. See also Lutz MacKenson's study in FFC, #49 (1923) and Child, I, 124-125. Archer Taylor (JAF, 1929, 238f.) discusses the American, English, and Scottish versions of the ballad. He concludes that the American texts follow the English tradition (see p. 243 ) exclusively. The beaver hat, the failure to call the hair yellow, and the introductory stanza are all English traits. For the Scottish traits (not common to America) see pp. 238—40.
The extremely wide variation of story types in America can probably be traced to forgetting of details combined with attempts to rationalize either the presence or absence of the "harp" motif with the rest of the narrative. Certainly there has been no printed text that has frozen the story, as is the case in other songs. Note should be made, in connection with this point, of the Gardner and Chickering, Bids Sgs So Mich, B version ("Peter and Paul went down the lane") which is scarcely recognizable as the same song.
Perversions of the original such as my Types C, E, and G (cf. Child B and my Type C in connection with G) are the results of small changes in some detail of the narrative. However, they reveal the sort of change that might easily create a new story if enough momentum were gained. For example, the Type A version in North Carolina and Kentucky (see Ky Folklore Record, 1958, 116) is ready to give birth to a new plot. Here the tale is told in the first person, first by the younger, then by the elder, sister. After the elder girl pushes the younger in the river, the miller pulls the younger girl out and is executed for the crime. The elder sister goes scot free. No mention is made of the miller's robbing the drowning girl. Type I has been melodramatized through similar alterations of detail, probably with the aid of forgetting. Types F and M are undoubtedly the results of omission of the ending in one of the other classes, though check the Cox, Trd Bids W Va, B text in which the miller is hung for pulling the girl to shore. Types J, K, and L have all been sentimentalized. J and K are certainly related to Child M, while K and L may echo the marriage feast that is present in the Norse forms of the story. Types D and H refer to texts that are well-known, D combining Types A and B, while H is paralleled by Child S. (Under Type J, see Garrison, Searcy Cnty, 20 who quotes his informant as saying "that they (some forgotten Vines) told how the miller and trie cruel sister, who had together plotted the younger girl's drowning in an attempt to get possession of property that had been left to her by her sweetheart, were hanged".) Type N resembles Type B in the use of the instrument motif, but seems quite corrupt at the start. Barry, BFSSNE, XII, 10 theorizes on this text. Type Q, from Virginia, is one of the finest texts collected in America. It resembles Child B, although it includes the "bow down" refrain of the Child R-S, U-V, Z series.
In general, the miller is present in American versions, although the grue¬some musical instrument portion is lacking. (See Child Y and the whole Rf. group.) The elimination of such a supernatural motif is in keeping with the usual American practice, and the New World mood is on the whole lighter than the Old. Flanders, New Gn Mt Sgstr, 4 points out that texts where the girl gets capital punishment are less likely to degenerate into comedy than those where the miller is hung.
The refrains of the ballad have been given a great deal of attention. For discussions of them see Barry, BFSSNE, III, II; Belden, Mo Fsgs, 16; Henry, Fsgs So Hghlds, 38; JAF, 1932, 2 ("bow down" refrain); and Taylor, JAF, 1929, 238. The usual American refrains are the "juniper, gentian, and rosemary" corruption, or a "bow down, etc.—I'll be true to my love, if my love'll be true to me" variation. Nonsense lines ("sing i dum", "hey ho, my Nannie") are also found, and Randolph prints a refrain "bonnery-O" which seems to come from "Binnorie, O, Binnorie" (Child C). See also BFSSNE, IX, 4 and X, 10 and the Morris, Fsgs Fla, texts. The latter songs feature the word "rolling" in various combinations.
Botkin in his Am Play Party Sg, 59f. discusses the refrain of the song and its use in the dance-game versions, and Thomas, Sngin Gathrn, 79 describes the ballad as a Kentucky dance.
The song is often found utilizing the "bowed her head and swam" cliche so common to Child 286.
For a detailed discussion of a number of American texts, see Zielonko, Some American Variants of Child Ballads, 30. Refer also to Barry, BFSSNE, III, 2 and XII, 10 for detailed treatments of the tradition of the song, especially in connection with Type N.
Helen Flanders and Phillips Barry   (see Ancient Bids, 163, Gl, G2) discovered a remarkable Polish text in Springfield, Vermont. In this song, the younger sister is murdered during a raspberrying contest and a flute is made from reeds at the grave. It seems to be a folk variant of the ballad Maliny, written in 1829 by Alexander Chodzko (1804-1891). Barry dis¬cusses this text in detail in BFSSNE, X, 2-5 and XI, 2-4. See also Jonas Balys, Lithuanian Narrative Folksongs (Washington, D.C., 1954), G7, 119-120.
Jeckyll, Jamaican Sg Stry, 14 prints a cante fable called King Daniel that follows the outline of The Twa Sisters and that includes a talking parrot.