being a stepmom myself, i will give you my point of this. How old is the girlfriends son. That does play a role. i am told i am harder on my stepson than on my kids with my husband. But my stepson is 8, and the other kids are 2 and 2 weeks, so there is a HUGE difference in how they need to be treated and what they know. If the son is around your daughters age, than yes there is a problem. What i would do, is encourage your DAUGHTER to talk with her father. She should be able to talk to him on the side with no one around and tell him how she is feeling about things in his house. if he doesn't listen to her at all, THEN i would step in. But you have to teach your daughter to stand up for herself. Even on things she is uncomfortable with.
My stepsons mom tried telling us things that he didn't like about here, but when we talked to him about them, he told us that he didn't have a problem and that his mom lied to us. We have encouraged him to talk to us about problems here. We have told him he can tell his mom as well, but if it's here, we want to know from him, so we can resolve the issue. So now when the mom tells us things, unfortunatly we don't really listen to it at all. We will ask him about things and it's always the opposite of what she tells us. So we have concluded that she is still very angry that I married her ex, and that she is very jealous of my relationship with the son. Since she never had relationships with her step parents she feels her son shouldn't have one with me either.
I don't know what you want to say are the father's responsibility, and not the gf's. In my house, if my husband can do it, so can I. I discipline and talk to my stepson all the time. I have been around since he was 1 though, so he has never known anything different in our house.
If you and the ex are on good terms why not have an adult meeting. Where all of you sit down and discuss everything. I will say that it's not always possible. I wish we could do that with my husband's ex, but that will never happen for us.