Your girlfriend is fortunate indeed to have found someone as sensitive as yourself who truly appreciates all she has managed to accomplish. You are correct not to try to parent her daughter at this point. There is too much that is unsettled between the mother and daughter.
I’m very concerned that your girlfriend allows herself to get into fights with her daughter. My guess is that it was just the two of them for so long that they developed more of a buddy relationship than a mother-daughter one. It’s very common and not something your girlfriend needs to be ashamed of. But if she wants to normalize the relationship in such a way that there is room for you to co-parent, she will need to take the lead to stop the fighting. She also needs to be mindful of the impact her fights with her daughter are having on your young son.
I strongly urge the two of you to find a family therapist who specializes in teen issues. Putting a halt to one kind of relationship and starting a different one is hard work. The two of you need a third party to hear some concrete examples of what causes the fighting and disrespect and to offer some suggestions to your girlfriend about how to make changes. Your girlfriend needs to learn how to be less reactive to her daughter’s provocations. You should go to appointments too because you need some pointers on how to support your girlfriend so she can do what needs to be done.
By the way: Nowhere is it written that parents need to fund higher education for someone who is disrespectful and unappreciative and who doesn’t pull her weight in the household. A college education is a gift and a privilege, not a right. As tempting as it may seem to get her out of the house and off to school, maybe you and your girlfriend should consider whether she is mature enough to be in college. It may do her good to work for a year and to gain a better appreciation for how hard her mom has had to work to provide so much for her.
If it would be too difficult to have her living at home, consider a “gap year” experience like City Year. That would give her some good experience in the real world and would add to her resume. Take a look at http://usagapyearfairs.org
I’m not for a moment suggesting holding off on college as “revenge” or a punishment. Telling her to wait shouldn’t be grounded in anger but instead be a wise parenting decision. She has some growing up to do before she is ready to take full advantage of the tremendous gift of an education.
I wish you well.