I don't think a 4th grader is mature enough to make the decision. Also, every child at some point wants something other than what they get. My kids at some point all wanted to go to school, and their PS cousins wished they could hs!
As for rebelling. She's going to... If not over school, then over something else. So you have to pick your battles. Stand very firm in the ones that are important! Don't allow her to rule the roost because you are afraid to cross her. I speak from experience times 10.. And I only have ONE daughter! She was the world's most rebellious, strong willed child. Sigh.. But she's 21 now and a joy. I, on the other hand, have many grey hairs and a top notch prayer life....