My fiancé has two children with his exgirlfriend. The eldest is not biologically his. She trapped him into a relationship by saying he was. However he was born of a different race than both the woman and my fiancé. He signed the birth certificate and gave the child his name. The younger child has never been dna tested but there is a possibility that she may be his. He pays child support for both children and is now being informed that he is also mandated to provide them with heath insurance because the mother does not work and takes advantage of many government assistance programs. What can my fiancé do to still be a part of his children's lives but not tied down financially to their mother?

Nothing. He has acknowledged paternity and is therefore, the legal father. Its probably too late to change that now, especially if he wants to remain a part of the girl's lives.

He can attempt to get full custody of his children.

If he is taking care of them day-to-day, then he doesn't pay child support.

what can my fiance do to still be a part of his childrens lives but not tied down financially to their mother?

He can do nothing. He was so stupid and now he must pay for his previous actions.DOT.That's the classical "estoppel" example.