"My mother is also a teacher."
Are you asking what is the difference between 我的妈妈也是老师 and 我的妈妈是也老师? Actually the 2nd sentence is a wrong one.
我的妈妈也是老师 can mean
- (same as another person) my mother is also a teacher .
- (in addition to her other identities) my mother is also a teacher
We need other context words to know the exact meaning.
It is all about the context. If it is already understood that the subject is "my" mother then 我的 can be omitted.
You are speaking to your sibling (you have the same mother).
You are speaking to your teacher (the identities being clear, vs. when you are speaking to a classmate and she has her own mother and confusion becomes possible).
"My" mother has already been the subject of discussion earlier.