Dear Anonymous,
Dishonesty already broke your whole family apart.
Your husband should get sole custody of his child.
That would leave you free to negotiate with the father of the other child for the expense of raising him/her.
I think, possibly depending on the state, that poor guy is on the hook for child support no matter what. There is a narrow window to be able to opt out once you find out the child is not yours. That period has past and that guy is on the hook till that kid turn 18.