I would provide ample time about when you need the stage. I spoke with our OAP instructor about three weeks ago needing the stage for a few days next week. She was fine with it and we even communicated about OAP UIL and Band UIL CSR being the same two days. We're going the first day and she is going the second. If communicating doesn't work you need to speak with the administration about doing what's best for the kids.
The kids will benefit from practicing on stage because 'x' reason. Know when OAP is performing and work together for the kids benefit. That's probably the angle that will work for administration.
Any advice on dealing with the theatre teacher who firmly believes the stage is only hers?