Asked: Help me identify this old anime movie / OVA…?

This is going to be a very choppy description, but please bear with me. I haven't seen this movie since I was six or so. All details are very hazy, so while I'm typing what I think happened, I may be completely off.
I remember it being a little sci-fi-ish. There are a bunch of young girls who remember nothing of their pasts being kept away from their parents and the outside world–they are being used for their psychic abilities. The main character is one of these girls, who proves to be quite a trouble maker. The main antagonist is a fat guy (I think), and his lieutenant is a cool-looking girl with pink or red hair. At one point the protagonist says her parents names (or she sees them or something), thus unlocking her memories.
Something happens and everyone must flee; the protagonist uses her psychic abilities against the antagonist as he's trying to run, and he tries to shoot her. The lieutenant takes the bullet instead.
They're in like a hot air balloon or something.

…And that's really all I remember. Whew. Glad we made it through that. I realize this is an insanely disorganized description, but I'd be very appreciative of any person that can help me.
This has been bothering me for years.