As to the significance of the phrase Lay the bent to the bonny broom, there was some discussion of it in this thread:

LYR clarify -- Bent to the Bonnie Broom?

Particularly useful is a message from Sandy Paton, quoting Lucy Broadwood and others on various esoteric interpretations.  It's worth mentioning, though, that Margaret Dean Smith had this to say on the subject (A Guide to English Folk Song Collections, Liverpool University/ EFDSS, 1954):

"The refrain Lay the bent, sometimes found in other contexts is sometimes glossed as a magical "herb refrain", but "bonny broom" has a physiological significance - and "bent" may possibly be glossed "horn" (cf. Chevy Chace), and the whole phrase interpreted in the lingua franca of amatory folk song."

In plain terms, a sexual meaning is just as likely as a magical one; probably more so.  In neither context would "bairn" make any sense unless one were to construct a whole raft of contrived "explanations" as to what the new phrase might mean!

Here is some further material on some of the many Cruel Sister variants, both traditional and revival.  I've stuck, as usual, to sites which seem likely to remain stable, and which offer generally reliable information:

In the DT:

The Twa Sisters  Collated version from Travellers' Songs from England and Scotland (Ewan MacColl/ Peggy Seeger); with tune.
The Swan Swims Bonnie  From The Scottish Folksinger (Buchan and Hall, 1973).  A collated text; tune from Belle Stewart.
The Cruel Sister  As recorded by one Dave Webb; appears on the face of it to have been learnt by ear from a Pentangle record, and re-cast without the refrain.  No tune.  If anyone knows anything about this one, I'd be grateful for any information -the tune is one of the "missing" ones that we're looking for.
Binnorie  From the Grieg-Duncan Collection.  Two slightly different tunes are given; both from Greig-Duncan?
Binnorie (Two Sisters) Version from Bruce and Stokoe, (Northumbrian Minstrelsy, 1882).  Four tunes given; the first is from B&S, but with no clues as to where the others are from.
The Two Sisters (7)  ?Collated text, with tune; from memory.
The Wind and the Rain  American version from Southern Folk Ballads (McNeill).  Collected from Dan Tate, VA, 1962; with tune.
Oh, The Wind and the Rain  American version as recorded by one Jody Stecher; no original source or tune given.
Two Sisters (Bonnie Broom)  As recorded by Frankie Armstrong, with tune.  No indication of original source; text is more or less the same as that recorded by Pentangle, with the same interleaved refrain borrowed from Riddles Wisely Expounded, though the tune is different.
The Two Sisters (8)  From Songs of the Newfoundland Outports (Peacock); with tune.
The Two Sisters (9)  No source named, no tune given.

In the Forum:

Minorie  As recorded by Ewan MacColl; apparantly learned from his father.
Binnorie - Icelandic version  Some discussion, plus a link to Norwegian versions (Dei to Søstre)
I'll be true unto my love  American version as recorded by Clannad.
dulaman/two sisters  Inconclusive discussion of Clannad recording.
RE: dreadful wind and rain lyrics  As recorded by Grisman and Garcia, (who learnt it from Kirby Snow) plus a short parody.
Two Sisters (Child #10)  Variants: Barkshire Tragedy, Grisman and Garcia (again), There was an old Jaynor (from Vance Randolph, Ozark Folksongs Vol 1) together with some discussion.
Two Sisters, Horpa  Norwegian version, with translation.
Rollin' a-Rollin' (Child #10)   Modified American version (Florida).
on a "two sisters" song  Further discussion of the US version recorded by Clannad.  Also The Little Drownded Girl, collected by John Jacob Niles from Patterson Whetmore, in 1932 on the steps of the Hatcher Hotel in Pikeville, Ky.
RE: Cruel Sister Two  Unidentified versions quoted from Child, E&SPP: the first is his version G, (Mrs. King of Kilbarchan; Motherwell's MS), followed by some lines from the version given by Thomas Hughes in The Scouring of the White Horse (1859) as quoted in Child's notes.  The second is Child's version H (I. Goldie, 1825; Motherwell's MS.)  Version from Hindman, Kentucky.  Short parody by "Fiddlesticks".
Twa sisters  Text as recorded by Pentangle, short American version as recorded by Red Clay Ramblers,
Lyr/Chords Req: the two sisters  Discussion of the set recorded by Bob Dylan; several half-remembered American versions; the Pentangle text again (twice); American text as recorded by Cynthia Gooding; version from Horton Barker (Chilhowie, Virginia, 1939).
Stupid Question--"The Twa Sisters"  Entertaining discussion on the practicalities of constructing harps out of bits of dead people.
Flanders ballad in Polish  Some inconclusive discussion of a Polish version.
An Bhean Udaí Thall  Several Irish versions of a Gaelic song, plus one tune; similar story, but not really a relative.

There is an entry at  The Traditional Ballad Index:

The Twa Sisters

There are a number of versions at Lesley Nelson's  Folk Songs  site:

The Twa Sisters  From Jamieson's Popular Ballads (1806); with tune.
The Barkshire Tragedy  Text and tune from English County Songs (Lucy Broadwood/ J.A. Fuller Maitland)
Child's versions A-U

At the  Max Hunter Folk Song Collection:

The Millers Daughter  As sung by Fred Smith in Bentonville, Arkansas on June 23, 1958
The Old Woman Lived on a Sea Shore  As sung by Mrs. Pearl Brewer in Pocahontas, Arkansas on November 12, 1958
Two Sisters  As sung by Mrs. Lizzie Maguire in Fayettville, Arkansas on June 23, 1959

As mentioned earlier, there are some 103 Norwegian versions at  Dokumentasjons-prosjektet  A Norwegian Universities Joint Project:

Dei to Søstre  (The Two Sisters).

Malcolm