Seat changes are such a big deal. If you need a certain seating arrangement, then yes it’s good to call and send an email.
The email is good for documentation purposes, just in case.
Yes have her call again for the seat change, in my opinion. If it will help you be a better student, then even if it’s another phone call, it’s worth it. Ask your mother to document or send herself an email of the conversation with the teacher with a time-stamp.
Okay this may be more than necessary, but it helps to have backup if you should need it later on.
B’Atzlacha 🙂