What are my leagal rights after my husband for 9 years abandoned me and our twins?

My husband walked out on myself and our twins four months ago. He has refused to see the kids. He moved into a new place and immediately moved his women in. He cleared out all our accounts and cancelled all utilities. He cancelled mine and my children's health care. We are on welfare health insurance. My parents paying our bills. He gives the twins 100 a week each in child support. He had paid the rent for the first three months but was always late we were threatened to be evicted twice. The catch is that I was previously married. I was legally separated and legally divorced as far as I knew. I received a call from my first ex after I was re- married for a year. He told me he never submitted the divorce papers. .So we were still married. I know he did not do this to cruel. He just had forgotten to do so. He was now getting remarried so I went in a signed the divorce decree. It was finalized and I was told by his attorney that my marriage was legal as we did not remarry with intent of knowing the divorce had not been finalized. My husband now is using it an excuse to say his kids are illegitimate and we never had a marriage..We were only in a simple relationship and he owes me nothing. I want to find a way no matter how to make sure we are legally married since he is using it in a malicious way. As he wants us to starve saying he is not responsible. He is lying with a Colombian woman on a school visa. He wants to marry her and therefore she could stay in the US. He said he can do this since we are not married. He lives with this woman while she goes to school and only works two days a week and he supports her while we starve. What can I do to rectify this situation. We are going to starve. I have found a job and only make minimal salary since I was out of work for years raising our twins.