You'd be surprised at how homophobic the figure skating world is... It's not like ballet, which is theatre, where sexuality isn't a big deal backstage. Perhaps it's because it's so competitive, I don't know.
So, this is not a movie, and people probably aren't all that into anime here, but speaking of figure skating, I highly recommend Yuri!!! on Ice. It really is a beautiful story, 12 half hour episodes, so not terribly long either. It's not so called yaoi, it was a prime time cartoon series on Japanese television, but it's one of the sweetest love stories I've ever seen. The skating animations are amazing, too. It's funny and heartwarming and hella gay, lol!
The whole thing is available to watch on Crunchyroll for free. All you have to do is make an account.