Your post lacks detail, but it sounds like the children were "placed" with you (other parent?) following an abusive situation. Was the mother the abuser?
If all this was done through the courts, wasn't the child support issue brought up at the time of placement? Is there a hearing scheduled for modifying the support order?
There should be no reason she would continue to receive child support payments if the custody is legally changed, even temporarily. Child support is to provide for the children, not the mother. Spousal support is a separate issue. In fact, it would seem she not only should not receive child support; but she also should be required to pay same.
If she loses her home in the interim, she could have a problem proving she can provide a stable environment for the children.