I would ask my parents why they thought I needed a different T. That I felt satisfied with the current T and need to know why they think this isn't working out.

I don't think the degree held by the T is all that important. My T has a superior reputation in my area, she teaches people how to be a T, and presents at conferences. She has a master's degree. A PhD wouldn't improve her abilities.

I'm sorry your parents are changing their minds so suddenly.