divorced once and now common law?????

I have been divorced from my ex husband since April 07, final decree Aug 07. He filed for the divorce when I got in legal trouble and went to jail, I was served in jail along with a PFA so he could keep our daughter away from me. It was dismissed and divorce was granted. He knew I planned on getting a divorce on the grounds of adultery, and when the judge said she would grant it that day I did it because of the emotion l stress. We began talking again for our daughter (special needs) sake. He would stay with us every few months for no more the 2 weeks at any given time. I started threatening to enforce child support in September 08 after a year and some months of nothing. I went with him to open a checking account so I would know how much/often he was depositing money. That did not last 6 weeks and little money was deposited. We talked of getting remarried when times were good but decided against it, mainly because he was the one saying never. In January 09 I finally went to DHR and started the paperwork to enforce his obligations and 4 days later I was served with NEW divorce papers. I did not finish the case with DHR because I did not know what to do and did not want to have other legal problems. He took me to court for this in May and got granted new custody arrangements until we came back 2 weeks later. Our daughter became sick and hospitalized so the judge put it on hold. He had his lawyer place in on administrative hold and recently set a new date for December 21. My question is how is getting all of this when he hasn't had to prove how we would fall under common law marriage. He was the one that never wanted to remarry but agreed to work on our problems for our daughters sake (she has a terminal illness). I have researched the criteria for a common law marriage to valid and we do not. We did live together but for no significant time. He never had mail or personal belongings with the exception of a few changes of clothes and a toothbrush. We did not introduce ourselves as man and wife but working on our problems. I moved out of the marital home in Jan 08 and the lease is in my name. I have maintained a bank account (my name only since 2006) and paid all bills and expenses (as well as the bills from the marital home he did not live in from 2006-2008). He has helped 2xs- $200 and $100 for the light bill, and in May09 when his attorney instructed him to give me at least 500 before court ( I received $200). I did keep his name for our daughters sake and we did get a vehicle (all money paid so far was from me including the down payment) in August 09 and we did it so I could transport our daughter to her dr's appointments (300 miles away 10-12 times per year) and other places she needs to go. His name is first mine second. All friends and family have heard and witnessed this behavior, us trying at times to work on our relationship as well as the way he would stay long enough to appease me and then he would leave and start drinking and staying at bars. Yes we had intercourse on occasion, but we both had relationships with others.
What should/can I do? He takes our daughter for weeks at a time, he will not pay child support or contribute to our daughters needs, and I don't believe we are common law married. Please point me in the right direction!

What state? Every state is different.