Here is some further background and history to the song, from our family Classics scholar:

Here is what has been posted on the Latinteach list ("ad usum delphini"
means for the use of the Dauphin, which is to say, G-rated, expurgated;
"Ad usum delphinem" (sic) means "for the use dolphin" -- a typo):
 

"What you may be missing here is some of the history of this
ditty, which is a version ad usum delphinem of what is found in Seutonius de Vita
Caesarum, 49.4:

<<Gallico denique triumpho milites eius inter cetera carmina, qualia
currum prosequentes ioculariter canunt, etiam illud vulgatissimum
pronuntiaverunt:
    Gallias Caesar subegit, Nicomedes Caesarem:
    ecce Caesar nunc triumphat qui subegit Gallias,
   Nicomedes non triumphat qui subegit Caesarem.>>

 I'll leave it to you to note the changes."

RJ's Translation: Then his soldiers in the triumph from Gaul sang, among
other songs, jokingly as they escorted his chariot, (and) they also(or
"even)  pronounced this very vulgar/disgraceful thing (this is according
to Suetonius, who wrote in the first century AD):

Caesar has subdued the Gauls, and Nicomedes has subdued Caesar;

(Note:Caesar was reliably reported to have had a homosexual affair w/
Nicomedes, the king of Bithynia in Asia Minor; Caesar was bi. On his
return from a mission as envoy to Asia Minor early in his career, he was
called "the Queen of Bithynia". Caesar's wife was supposed to be above
suspicion but Caesar himself was a prolific source of sexual scandal, far
more varied than Clinton or any modern politician, and he never had to
apologize.  Rome never had Puritans, although periodically someone would
raise a great hullabaloo about traditional Roman values like piety and
virtue, and the terrible decline of morals. RJ)

Behold Caesar now rides in triumph who subjugated the Gauls,
Nicomedes doesn't ride in triumph, who subjugated Caesar.

Apparently there were various dirty verses in the ancient world, which I
don't know.  It is probably safe to assume that some of what remains is
ancient and much of it not.

(See, I haven't totally wasted my time all these years. Thank God someone
actually asked about something I could answer!)