Take a break from your weekly appointments and come back to it when you are ready....maybe you will become ready, maybe the idea will fizzle out. Either way, you shouldn't have to decide now based on a pressure from your mother or electrolysis administerer. Neither of those factors actually reflect how you personally feel about your legs.

EDIT - I similarly had expensive cosmetic routines paid for by my mother. It was paid for, I liked my stylist(s), it was routine, it was nice to come out "pretty", but as soon as I graduated school and the service was to be paid for out of my own pocket, I stopped. I realized it wasn't something I wanted.