What a sad and confusing situation you’re in. You and your mom are both trying to do the right thing and give this girl a safe place to be. On the other hand, it sounds like you wouldn’t be with this girl at all if she wasn’t pregnant.
You probably won’t make good decisions if you don’t have good information, if you feel pushed into a decision, or if you feel trapped. However, your girlfriend does need help and the decent thing to do is to help her find it.
I suggest that you find out what supports are available in your area for pregnant and unwed women. You could ask the pastor at a local church or your doctor for the names and phone numbers of places that are set up to help unwed mothers. Some places also understand that unwed fathers also need support. You certainly aren’t alone in your situation. If you ask, you may find more help.
Please find out from a lawyer what it means for you legally in your state if you sign the birth certificate. (Usually it means that you are obligated to pay child support until the child grows up.) Think about asking for a paternity test when the baby is born to settle the question of whether you are the father. With that information, you can make more informed decisions.
Finally, remind your mother that you can’t make a relationship with someone because your mother loves her. You need to love her at least as much as she does. If the baby is yours, you will want to stay connected with the mother and your child. You might even give the relationship a chance. If the baby isn’t yours, you can at least be a good friend and help her out during a tough time.
I wish you well.