I would absolutely give her a choice.
I LOVED summer vacation when I was a kid. I loved being able to decide what I was going to do each day, and not having to spend each day doing what someone else thought I should do. It was the only time I ever felt I had any freedom, and it was awesome- wish I could go back :)
I spent time reading, playing with friends, riding my bicycle, running through the sprinkler, buiding forts in the woods with my brother, damming up streams (they were really small), looking for tadpoles, drawing/ coloring, trying to catch fireflies, puzzles, games, Rubik's cube -loved the 80's ;)
I'd add more, but this list is getting too long already-sorry, got a little carried away reminiscing...
Have you asked her what she'd like to do if she didn't go to summer school? Maybe she's not yet sure herself, but I would just let her know ahead of time what the limit will be on tv and computer/ video time. She might not know what to do with herself at first, but I believe that's when kids start to learn to be creative and learn how to entertain themselves. Or, she might just surprise you and come up with ways to spend her time easily.
Also having some control might help to alleviate her anxiety problems. Some kids (like me, my bro, my oldest son) are stressed by too much structure. Rather than being happy to have "something to do", it feels too stifling for us.
Anyway, for what it's worth, that's what I'd do.
Blessings