In an emergency situation anyone may preform a baptism for another and it can happen anywhere. Delivery room nurses are often trained to do so where the new-born infant is not expected to survive more than a few minutes. All Christians reject baptism for the dead.

Believers in adult baptism should be baptized by their minister, whomever that may happen to be. In a home church the role of the minister should be that of the father as spiritual head of both family and (in this case) church.

In my opinion, while it's fine for a mother to teach children the things of God, a mother can never be the spiritual head based solely on her gender. She must always defer that role to a male, preferably her husband. Here we look at "adult" baptism in a non-emergency situation and I would be extremely uncomfortable with a female usurping a role which she is forbidden to exercise.