My husband and I are getting ready to go through divorce and he is on disability? Do children keep benefits?

When a husband and wife divorce, do the children keep their benefits when the husband is the one on disability and the wife is the custodial parent? Also, if they do keep their benefits, is the wife still able to collect child support from the father? He is working part time, getting paid cash for his work....how can I prove he is making this money so this money can be counted on to collect support?