Did you say that your girlfriend’s not Catholic and that her mother wants to convert you to the Baptist faith?
If your girlfriend’s not Catholic, (if I understood what you said correctly), that’s actually a bigger problem than your potential future mother-in-law’s trying to convert you.
Well, with your girlfriend, should you ever get married, in the best circumstances, you’ll probably going to separate churches on weekends. If she allows you to take the children to your church, then you and your children will go to your church. Would she stay at the house or go to a Baptist church while you are doing that?
If in the future, you want to use Natural Family Planning, rather than contraception, would she be amenable to that? Will she allow you to have rosaries, a Catholic Bible, crucifixes, religious statues and prayer cards at the house?
If you go to confession to a priest, and take the children with you, will she be okay with that?
You would be expected before marriage to attend Catholic marriage preparation, Precana. Would she be willing to do that with you and marry in a Catholic Church?
Will you get resistance from her family about your faith and that of the children later on?
I think in all probably that your family will probably be split on the issue of religion.
Will you be able to pray together. Will she ever attend mass with you and the children?
So, your girlfriend and girlfriend’s mother will both be “on the same page” against you, right? Two against one. That sounds like it’d be very uncomfortable, more in the future, after marriage, when the honeymoon’s over.