I think that a set of gay parents in a Disney animated film could theoretically happen, but honestly, the only way that anyone would know is if the child referred to both parents as Dad. You don't see parents go off to bed together or kiss in an obviously romantic way in almost any animated films meant for children -- the only two that I can think of are the Lion King (Mufasa and Serabi wake up in the cave -- in that
really strangely monogamous pride of lions.
), and I think that the one human couple that we see in that situation is in Lady & the Tramp, at the very beginning when Jim Dear tries to kick Lady off the bed (and that's an odd one, too, because in that era with a family with that much wealth, the odds are they would have had separate bedrooms -- AND household help!)
The thing is, Disney animated films are meant for
young children, kids who are so young that sexuality is not really something that has meshed in their minds yet. We all know 4 y.o. boys who like trying on high heels and wearing wings, and who grow up to be flaming heterosexuals anyway. (And no, I'm not saying orientation isn't present at that age; just that healthy pre-pubescent kids are not thinking about sex -- the average 4 year old doesn't know what sex is, and if you explained it in detail would be disgusted.) Healthy young kids think of "love" in terms of hugs and holding hands and kisses on the cheek. They don't think twice about dancing with anyone who happens to be dancing, or holding hands with or hugging a friend of any gender, unless some uptight adult tells them that they shouldn't. They don't automatically see two people sleeping in the same bed and think "romantic partners" -- they think sleepover. Now, besides that, how many nuclear families are there in Disney animated films in any case? Very few, because nuclear families don't make for very dramatic stories unless they happen to be superheroes. Having only one parent around makes life much simpler for the writer in the world of family-oriented drama.
As to the Prince/Prince thing -- sorry, that one makes no sense, assuming that you want them to have a legally sanctioned monogamous relationship. Royal marriages are by definition dynastic, so unless the person was so far down the order of succession that they really don't live that "castle" lifestyle, any marriage that they made would require legitimate heirs of the body, which wasn't exactly possible for a gay couple in the 18th century, or even in the 1920's. There have been PLENTY of real princes in history who preferred men, but they either didn't marry at all and left the succession to a younger sibling, or had those relationships on the side, because the whole point of marriage in that mileu is the production of heirs. A prince who wanted a same-sex long term relationship and was unwilling to make a dynastic marriage of convenience wouldn't be looking for another prince, because that prince would be in the same boat. He would be looking at someone who didn't also have a succession issue to worry about. So, unless you are advocating that an animated children's film with a historical setting get into the logistics of how to have sex on the side, I'm thinking that it really isn't workable as a plot in this context.
Now then, we all know that Disney doesn't just make animated films. I think that you will definitely soon see openly gay characters in live-action films that are meant for an older audience, but you won't see them released by Walt Disney Pictures or Pixar. Disney segregates their production companies by target market, and these days WDP productions are firmly in the 7-and-under marketplace. It wouldn't surprise me at all if Princess Mia has a third cousin who is living happily ever after with a same-sex partner.