I can appreciate that you are trying to work on this challenging situation, but it is a tough one. I personally believe this very young woman is getting emotionally serious and having sex and children without an awareness of the very long term consequences. Why is the baby with the Mother in law, what about you- people support their children and work, maybe an arrangement can be made to successfully include your very important parenting of this child.
Sounds like the girlfirend needs to be ALONE- then get paternity test, then stay ALONE for a long time until she matures a big amount. I know I sound harsh, but this is a very young woman and older men can certainly make decisions regarding sex and birth control that may be effective. I hope you will communicate as well with her and her family as you have here in your post regarding your child (children?) so the kids have the support they need. You sound really capable here.
And I am very sorry for the emotional pain that you went through with this relationship. Let us know how your situation unfolds, I hope you are able to work these issues out for the best. terri