The best ones I recall were at Topolino's (dinner). We had the Peche Repose: Peach, Mint, Lemon, Soda Water
Topolino's is a bit pricey, but one of the few places we felt was worth the price. It is slow meal, but the view is great during the fireworks. On the DDP, Topolino's is listed as 2 credits. I'm not sure I'd say it si worth 2 credits, and the menu is not very long, but if you can find options you like, the food is excellent.
I had one that was also decent at GF Cafe, but it was listed as a 'zero-proof' cocktail. Even though it was zero-proof, only adults could order it. I don't see the one we had listed on the current online menu. It was a fancy lemonade, including some type of zero-proof spirit. So I don't know if that would be okay for your family member.
Some of the options are at least listed in the online menus.
OH- I have not been there yet, but I was looking at pics of food at the new Japan eatery, and it looks like they have some mocktail options. I have no idea if they taste good, but the images look fun. One is a Yuze lemonade.
OH- not quite a mocktail, but Universal now has a popsicle stand with excellent popsicles in the Minions land. They have mango, strawberry, lemon-mint, and some character themed ones. All the ones we tried were really good, very fruity and refreshing.