I've been somewhat troubled over the last few weeks by Rabbi Steinsaltz's understanding, brought by @mbloch, that seems to say that the sages' tradition of what had conspired at the time of the making of the Targum was had been deeply distorted (from the name of the grandfather of Philadelphus to the name of his wife). However, I think I have a theory now about that, which may also answer the OP.
While the Letter of Aristeas, considered by academics the prime source of the story of the making of the Targum (sadly academics often are quick to write off Chazalic sources...), states that the Ptolemy of the Targum was Ptolemy II Philadelphus (in one place mentions Ptolemy son of Lagus, and when referring to the king, writes about Ptolemy, husband of Arsinoe his sister - this was Ptolemy II), the Chazalic sources never state which one it was, so per p'shat - it could either be Ptolemy I or Ptolemy II.
However, neither of the Ptolemys had any wife or consort named "lagína" or "lagoudína", the feminine forms of the Greek word for "hare" - "lagós" (per Wiktionary).
As stated by @mbloch, Ptolemy I's father was named "Lagus", which is very similar to the Greek word for hare, "lagós". His mother was named Arsinoe.
And as it turns out, there are three Tannaic sources that have slightly different versions of this tale:
Yerushalmi Megillah 12b:
"ואת הארנבת את צעירת הרגלים אמו של תלמי המלך ארנתא הוות שמה"
Translation: "and the [female] hare - and the hairy of legs the mother of King Ptolemy was named Arneta."
Vayikra Rabbah 13:5 (also appears in Yalkut Shimoni 536):
"וְאֶת הָאַרְנֶבֶת, זוֹ יָוָן, אִמּוֹ שֶׁל תַּלְמַי אַרְנֶבֶת שְׁמָהּ."
Translation: "and the [female] hare, that's Greece, the mother of Ptolemy was named Arnevet [hare]."
It's entirely possible that Arsinoe, wife of Lagus, had been nicknamed "lagína" or "lagoudína" or something similar after her husband. Per this, it seems that according to p'shat, the king of the Targum was actually Ptolemy I. However, one could also say that when Chazal say "mother of Ptolemy", they mean figuratively: "mother of the lineage of Ptolemy" or "mother of the dynasty of Ptolemy".1
Thus, as @mbloch pointed out, to call the mother of the king or of the dynasty an impure animal - and with no less than a nickname that might have had negative connotations (being that Lagus doesn't literally mean rabbit - see here, pg. 79) - would have seemed mocking on the part of the Jews, hence the need for the change. Therefore, it seems that there was only a slight distortion/scribal error in the Bavli's version (although admittedly no MS version on the Genizah's site can back me up on this...) - from mother to wife.
1 Both identifications have merit because both are descendants of Arsinoe wife of Lagus, and per calculations by Dr. Chaim Chefetz in his essay "The High Priests In The Beginning of the Second Temple Era", the High Priest during the end of Ptolemy I's reign and the beginning of Ptolemy II's reign was Rabbi Elazar ben Charsom, identified with Elazar the High Priest in the Letter (see here). Furthermore, both are known to have been involved with the Library of Alexandria, which, according to the Letter, was why the Targum was created. Ptolemy I built the library and his son promoted it and gathered many works there.