Q. 1. What is the Mother Church? Would that be the Vatican?
A. 1. The Vatican is the "Head" of the "Mother Church." The "Mother Church" is another name for the "Catholic Church".
The Rites that are in communion with Rome, they are part of the Mother Church. Being in union with the Mother Church, they cannot be called sister Churches to the Mother Church. They are the Mother Church.
At present, there are about 30,000 different religions in the world. With the exception of the Catholic Church and its Rites, all these churches are sister churches to each other. They are sister churches because they are either breakaways from the Catholic Church, the Mother Church, or were founded by individuals who's beliefs were based on those of the sister churches.
So when you hear a reference to the Mother Church, it is a reference to the Catholic Church.