I'm sorry your mom is hesitating on this. You are so forward-thinking to realize you can save the money in order to have a cushion for weeks when you have fewer hours. That is very mature of you! I wonder if you could also assure your mother that, should you come up short of $$, you will take responsibility for canceling the appointment ahead of time so that you don't incur a charge (although hopefully this won't happen).

You have a really good perspective on how valuable therapy is to you, and I'm impressed at your willingness to work for it.