No this is not child abandonment. Child abandonment occurs when a child is left without adult supervision. In a few states, child abandonment is used as a charge when a parent does not provide support for the child, None of that is case here.
What IS the case may be fraud. If the child is living full time with someone other than the mother, then THAT person is entitled to receiving support payments.
So what your husband has to do is get proof that the child is in the care of another person. Their testimony should be sufficient. His next step depends on who he pays the support to. If he pays it directly to the mother, then he needs to go back to the court that issued the support order and ask that it be changed to the actual caregiver. If he pays support to a support agency that then forwards the payments, he can ask them what is necessary to get the payments routed to the caregiver.
None of this is grounds to stop his support. As long as the child is a minor it is entitled to have support from the father.
Frankly, I think its shameful of you to try and get support terminated. Clearly this child is not getting the care its entitled to and THAT should be your focus, not trying to get its father off the hook. In fact, I would be trying to get custody of the child.