Separate from this girl. Give her time on her own to get her life together or not with you out of the picture. You or any other male she is involved will hinder this. She may be unable to stay away from the opposite sex and remain unentangled, but that is what she needs to do, until she is spiritually healed. When the powerful emotions that always come along with romance are working it is impossible to turn off the hormones that caused the problems in the first place. You are not her savior. Jesus is.
Grandfather, as always, is spot-on.
These broken home issues need to be addressed, and unless you’re in the emotional and spiritual position to protect yourself from a highly destructive co-dependent relationship, I would step away. Those skills take years to develop, and often come very late.
As far as I understand it, if you do break up with her, you’re going to hurt her, and that’s the last thing you want to do. She may not understand any reason you give her, and she may act out on her pain. Many folks think that "because I am in pain, I am entitled to poor behavior that hurts others and/or myself. That may be her version – unknowingly – of emotional vampirism.
Don’t be blackmailed, because you are not responsible for her reaction. A good way to back out slowly is to say, “look, here are these issues that we have between us, and I’d like to bring the relationship down a notch or two.”
Your intentions may be noble but your reservations are warranted. Down the road, if she converts, that’s not a magic pill that her life will get better because she has faith. Her behavior patterns, coping skills, and defensive reactions won’t change because she’s found Faith. It’s going to be an arduous process for her, and you have to watch and support without being sucked in.
Again, if you’re in the position of strength, not just in faith or morals, but have a grounding in psychology to get her the help that she needs and keep yourself from being hurt or hurting her progress, go for it. But that’s a tall order that many people aren’t equipped to deal with.
As far as gettng her to counseling or therapy, it’s expensive and there are many avenues to try out before there’s one that works. The mental health profession (from different therapies to medications) isn’t one-size-fits-all. It takes a lot of time. And she has to be willing to do it for herself, not for you or your relationship. (You can lead a horse to water but you can’t make it drink.)
If you continue to develop this relationship where you get to the point where you consider breaking up the relationship unless she gets help, then you’re at a point of putting all the responsibility on she who already isn’t strong enough to manage her life skills, and until this time she’s been depending on you.
That’s a tall order.