Lisa, I can tell you from experience, I've heard this story so many times. I've seen it work out a couple different ways. I've seen the mother pursue child support, and then battle the rest of her life with a man who is flaky, untrustworthy, and emotionally draining to work with. I've heard so many single mothers say "I wish I didn't have to deal with this, it is so stressful!". On the other hand, I've seen situations where the mother just let the father go, and didn't pursue financial support. Yes that put strain on her financially, but time and again I've heard women express that struggling to make ends meet is a different kind of stress than struggling with a father who's integrity and character are lacking.
Personally, when I came to the realization that the man who fathered my child (before I met and married Jon), was not interested at all in being there for me or my baby (financially, emotionally or physically), I cut the strings. At first it was scary. I had no idea how I would make ends meet, how I would support a child all by myself. But things always worked out, we always had enough. And 12 years down the road, I can't imagine how having someone like him in my life would have drained me and stressed me, (not to mention having to co-parent with a practical stranger, someone who's core values were obviously not mine).
Now, I don't know if your daughter has any relationship with him, I got the sense that there wasn't much of a bond there. I'm a firm believer that kids need healthy, balanced, loving people surrounding them. It sounds like you and your parents are more than sufficient in these areas. If it's money you're worried about, I say no need to worry. If you've read my story you know the ways that you and your child can have all your needs provided for and more! I also think if he is struggling to have a healthy life, it may be best to "cut the strings."
This is an important decision and I think deep down, we always know what is best for our kids. I know what worked for my life, and I have heard several women say it worked best for them too. But still, you have to weigh this decision carefully, and go with your best gut instinct.
Please keep us updated on how things turn out, my family and I will be praying for you during this time, that you'll be able to make the best decision possible.