The mother want to sign her rights over to a family member and the father/ her husband (they are marryed but not together, even live in to different states) has only been in the child life off an on for about a year and only sent $100.00 and the child is 16months. My ? Is if she signs her rights over to a family member does the father have a say or rights?

Think about it: if she "signs over her rights", that doesn't modify his rights at all.