If she is properly trusting the father with the baby, then she needs to have a life outside of her child. Assuming that the father is responsible enough to take care of the baby, the mother should have little concern in the case of an emergency, as the father should be able to handle it. If this is the case and the father is trustworthy, I understand where OP is coming from - becoming a parent doesn't mean that life everywhere else can stop.
But here's the thing OP - you got involved with a woman who has a child. Her first priority is the child, and if she is even slightly uncomfortable leaving her child in a different city, she will not leave that city. I'm not condoning this, as when she is not in charge of watching the baby, she should go out and do things for herself. However, she is just being what she considers to be the best mum she can be. You can't fault her for that.
If you are considering breaking up with her over this, it is understandable. You can't blame her for the fall in the relationship, but it is reasonable to say that it isn't working out for this reason. It's not fair that you always have to travel to be with her, when she cannot/will not travel to see you.
Also, please keep in mind that even though she has a baby and has clearly had sex, maybe she isn't ready for that sort of relationship again. Depending on how old she is, she may have realised what trouble sex got her into last time. Obviously this may not be the case, but I've found that whenever my friends have gotten pregnant and had kids (keep in mind we're 21+), they haven't wanted to risk having sex again until they are in extremely stable relationships.
Just my two cents, good luck!