I can't imagine the insurance company having any policy about scheduling. I think your T is misinterpreting something somewhere, especially since your son has a standing appointment. You could call your insurance company and ask.

It took a few weeks or so to work into her schedule, but I requested a set time and day each week so that's what I do. She works late, until 9 or 10 sometimes. My appointment is early in the evening. Sometimes she will call if the person before me cancels to see if I might want to come in earlier, and I'll do that if possible.