Hi mmasseychase, and thanks for the input.
We've definitely thought a lot about everything that we have to deal with in order for this relationship to work, and we've decided that the best approach is to start over. My girlfriend told me that she needs time to figure out how she really feels about me so we're taking a break from living together. It's not a break so that we can see other people, just a break from each other. Fortunately she has no interest in forming a romantic relation with the father of the child, and I accept the fact that he wants to be a part of the child's life.
My girlfriend has told me that she wants to be with me, but not if the relationship continues to be a bad one, and I agree with her. It is definitely best for the children. I am optimistic about starting over with her. I think some time apart will give us a chance to realize why we fell in love in the first place. And in addition to spending some time apart, we will also be attending couples counselling to work on some of our problems.
Thanks again for your input.