Y.N.
I don't really think you need a lawyer. I think you need to maintain the agreement as set. He sees her when he wants within the parameters set and don't worry about meeting the girlfriend. If she's not around your daughter, it doesn't really matter. You live your life and take care of your baby.
His relationship with your daughter is not your responsibility. As long as he's playing by the rules and your daugther is not in danger (danger being not just physical, but developmental, emotional, etc) than you should just limit your focus. When daddy is going to see her, be excited and say, "You're going to see Daddy!" And in your communications with him, let him know that you are taking responsibility for your role in her life, and you're leaving the responsibility for his role in her life to him.
We always want our children to have great access to great dads, but when we try to create the situation we take on more than what we should, add stress we don't need, and I think it actually undermines the goal and the dad's just pull back more because they don't feel like dealing with our perspective that, whether it's right or wrong, is still ours and usually unwelcome.
Ultimately, A., what I have learned is that there are no magic words or actions we take that will make the dad's suddenly wake up and fly right. They are going to do what they are going to do. All we affect is our own levels of stress. And by just letting him be, he has the opportunity to stop being defensive and therefore, possibly be reflective and make changes not because you told him to (they hate that) but because he feels he should.
Try being supportive, sympathetic and compassionate when given the opportunity. If he feels he has an aly in you, he may feel less inhibited in reaching out to his daughter and may be more receptive to advice that's not judgemental but caring. And remember, men too get sucked into unhealthy relationships that make them learn and grow, and sometimes just for a time, a learning time in their lives. I know that I had a horrible relationship with a guy who really abused me (verbally) and manipulated me. I am stronger because of it, and nothing anyone on the outside did could make it do any thing less than run its course.
Don't be stuck in the here and now. Life is happening to him, and things may change drastically in a year or two, which is a long time, but within the context of a lifetime, not so long. In the context of your stressing over this thing you can't change though, is a very long time indeed.
Just make sure he's doing his part - including sending you your support - and don't limit his ability to support her activities if it's not necessary. If you do feel you need a lawyer (who am I to say?) check with the University of Pennyslvania. They have a community law program connected with the law school.
Hope I helped!