I'm afraid I have to disagree with many of the posters here...let me ask you a question first.
Why are you choosing specifically Gay Days to come to WDW? Disney welcomes you any time during the year! There aren't any blackout dates for gay guests. <g>
As for vulgar or obnoxious things, and considering the age of your daughter and partner's niece, you will have to be prepared for the possibility of explaining certain words or expressions on red shirts.
You see, at one time a simple red shirt was all you needed during Gay Days in the parks. It was like, "We're here, we're queer, get used to it." Well, they (straights) did get used to it. For that reason, I believe, over the past 8-10 years now, based on my trips to WDW during Gay Days, most gay guests put expressions or even images on their red shirts, as a plain red shirt no longer has the same effect.
Waiting in line is probably where they will notice them most, considering the layout of most ride queues.
Most expressions are cute like "Furozen, Let It Grrr" (yeah, we get it, we knew you were a gay bear the moment we looked at your hairy, overweight body with the ubiquitous bear claw/bear paw tattoo, facial hair and shaved head) or clever, "I pay taxes, too," but some can be downright offensive. Some of those expressions, which I saw during Gay Days 2014, are so vulgar that if I were to put them here I would be violating the disboards' TOS. (Send me a private message for some examples.)
Finally, I'm an AP holder, go often, and I can safely say that I've never seen, any other time of the year, any guest wearing a shirt with an offensive saying on it.