You say that you think that your girlfriend is less invested in the relationship than you are, as evidenced by the fact that she doesn't want to commit to buying a house with you. You need to clarify whether you are reading her correctly or not. For all we know, she doesn't want to buy now because she stands to inherit a house soon. Or, maybe she doesn't want to move too fast because she has her own fears regarding intimacy, commitment, and so on.
The only way you are going to know where you stand is to ask her for clarification. To do this say, 'I notice that you resist buying a house with me and I wonder how I should interpret this. ' Then, you can throw out what you think is the reason for her resistance by saying, 'Am I correct in reading your resistance to purchase a house with me as a sign that you aren't sure that you want to commit to this relationship?' Then, sit back and see what she says.
Once you get the facts, you will know where she stands, what her issues are, and if they relate to you and the relationship or not. Keep in mind that if you have a history of giving more than you get in relationships, or of being rejected or unresponded to, this will taint how you interpret your partner's actions. So, let her tell you what she wants you to think or feel about her reluctance. Listen and understand her thoroughly.
Meanwhile, you need to focus on the fact that your needs aren't being met in this relationship. It doesn't sound like this woman is highly concerned about what you need for yourself and your daughter. It isn't clear if her inability to be accomodating exists solely around you and your daughter. Perhaps she's jealous of your attachment to your daughter and unconsciously wants to drive a wedge between you and her. If living on the wrong side of the tracks means that you can't see your daughter, and your girlfriend isn't willing to arrive at a living arrangement that makes these visits possible, then what is she saying? You need to ask her.
We also need to find out if her lack of accommodation is indicative of a personality style that extends way beyond thisissue of your visits with your daughter and the rent versus own question. Is she selfish (like nobody else's needs but hers matter); is she unyielding (that it's my way or the highway); and/or is her reluctance to buy telling you that she has too much baggage to commit. You are going to need to ask lots of questions and then make the proper assessment.
It may be that your marital discontent led you to test the waters before you jumped ship. I know you love this woman, but do you know her? Did you two discuss important life decisions before moving in, such whether she wants to marry and if so when? Did you discuss where you would live and whether you would rent or own? What about how she feels about your daughter? Will she make room for your relationship with your child? Now is the time to find out all about this woman.
If you find out that she isn't willing to make room for your daughter, then you are going to need to decide if you are willing to sacrifice your relationship with your child for someone who may not even be willing to commit to you. I would also suggest that you use my tests to help you assess this woman. The Ready for Love? test will help you figure out if she is, in fact, ready for a relationship. And, my Compatibility Test, version one (this version is taken by only one of the partners), will help you assess your level of compatibility in all the areas that matter.
I have a sneaking suspicion that there is a lot that you two don't know about each other. The test will help you pinpoint all these vital areas, so that you can go back to her and talk about them. Once you are armed with the facts, you can decide what is best for you and your daughter's future. Good luck.