There is another context. A person might not be in a school at that moment but she goes to school. For that meaning, I would say, "She is in school." Whereas, "She is at school," means she is in a school now.
Could "Dia di sekolah" be used for someone who goes to school but is currently on vacation?
"Kamu di sekolah" would translate to "You're at school". "Ada" in this context means to exist within, so, "You exist at school", which would then be more naturally "You are at school"
You would definitely exclude the "ada" 9 times out of 10, but having it is more formal.
(I hope this helps)