That would not make much sense and might ruin the beginning of the working relationship with the new teacher (unless he knows and approves). It seems your mother wants to make the decisions on your lessons? I don't know how old you are, but if you have no control over the matter our advice won't help much...
My mother is rather unsure about this as well. The thing I'm concerned about is that if I don't tell any of the teachers, then the assignments may overlap and I won't be able to handle it. Also, there's of course that possibility that the new teacher may find out ,thus possibly impacting the relationship.
That and your learning may suffer because teachers have different methods and concentrate in different things on different times and that may be very confusing.
It troubles me though. If I were to leave before actually finding another teacher that I wished to stay with, then there's a chance that I may later regret the decision to move on in the first place. But as stated before, learning with two teachers at the same time has its own complications.