If you have similar squad sizes you could assign every girl a buddy from the other team. You could do buddy conditioning, buddy games, and relays with your buddy. The second day could be twin day for the buddies where they have to dress the same. Take it a step further and when you play in football or basketball season, they could bring their buddy a little gift on game night. Your teams could also tailgate before the game together.
Another idea is to group up the classes and make them do a mini routine like they do at Hot Shots camp. Seniors from both teams, juniors from both teams, etc. Unite the classes even if they are at different schools.
A fun thing we did way back in the day was capture the flag. You could do seniors & juniors vs sophomores & freshman. Really any game that involves teams that you can mix the schools together in some way would work and be fun for them.