You're quite right about the possibility of some kind of dispute between the family members; as it happens so often even in our day, there is no reason to believe Irish nobility of the renaissance was in any way spared from it. Quite the contrary. If that was the case, was it enough reason for the Aylmers not to include Mabel's name, if she were their daughter, however? That seems to be the million-dollar-question…
Thinking about it, I remember there was indeed a dispute around this time and concerning this family, regarding the maternal grandfather of Julia Nugent, Gerald Fitzgerald, the 11th Earl Kildare. In his Wikipedia article, there is mention of his wife - incidentally also called Mabel - who "/.../ died in 1610, much troubled in her last years by a lawsuit brought by her grand-daughter Lettice, claiming that the Earl's will had been fraudulently altered." Lettice is also the 'alter ego' of Julia, the daughter of Gerald and Julia who married Barnewall; different sources seem to have different names for her, although as far as I can see they're always referring to the same daughter (i.e. the one who married Barnewall). In this case however I think the dispute might have involved a sister of Julia Nugent (the wife of Gerald); Lettice seems to be a name inherited in the family.
As does the name Mabel in these families, during this time. The 11th Earl's wife, as well as a sister of Julia Nugent bore the name; making it likely that if there was indeed a second daughter in the Aylmer family, she would have been a daughter of Julia and not of the first wife. I also don't really see any reason why the sources would be wrong about the lack of issue from the first marriage. On the other hand, if this is a case of 'wishful-thinking-genealogy' and that Mabel is a 'made-up' daughter of Gerald and Julia Aylmer, Mabel would have been a good choice of name, since its origin in the family lends the notion some credibility.
