@Renee93,
1. Stop fighting the father of your daughter about visitation or custody. A father has the right to see his daughter. Think of it this way, your daughter has every right to have a good relationship with both her father and her mother. You are hurting your daughter when you fight about visitation or custody.
It is up to both you and the father to be reasonable in raising your daughter together. Cooperate as best you can, and if you must go before a judge, you should still be civil and accept the judge's decision. Having to go before a judge for custody issues is a sign of bad parenting.
2. The issue of child support is completely separate. In my state (and I believe most civilized states) the law is written this way. Again, if you and he are even the slightest bit reasonable, you apply this formula to come up with an amount... and then you and he stick with it.
If you already have a court ordered child support he isn't paying, it is pretty easy for you to win (it goes state by state, but almost all states are pretty good about enforcing child support). If he is saying you will have to pay for his lawyer fees... he is full of crap. Judges don't do that. Go talk to your own lawyer... you can pay a lawyer $100 for an hour consultation and it completely worth it to have the information about what you can do. Don't be intimidated.
3. My advice is to be reasonable with custody and visitation. This is the father of your daughter. The better their relationship and the more responsibility the father takes, the better her life will be. The less you fight this, and the more you cooperate to raise your daughter, the better.
My advice is to hold the line on child support. If you have court ordered child support that he isn't paying, there are ways for you to get the money owed. Judges don't like people who don't follow their orders... you can almost certainly win the amount owed, and maybe more in penalties.
Many States will take child support directly from the paycheck of people who don't pay. Talk to a lawyer.