The way the system works is this.
Two scenarios:
If your daughter is on Income Support (IS) she should be declaring all payments to the DSS.
The DSS are required by law to chase the absent parent for CSA payments for each claimant who is on Income Support.
If there is a mutual agreement for maintanence, the DSS are still entitled to know about this, however your daughter would be able to keep a small amount, up to �15.00 I think at todays rate. The rest would be deducted from her IS>
If your daughter has one child to Joe Bloggs and claims �100 per week in IS for herself, her child and the familiy premium yet receives from Joe Bloggs through a mutual arrangement a payment of �25 for the child, your daughter will keep �15.00 of that and her benefits would be reduced by �10 weekly.
If your daughter didn't give the name of the father to the DSS or refused to then the DSS can take a payment from her �100 per week, equivilant of what they might have claimed from the absent parent.
The only exception to the above is if the mum and child is in a very difficult situation through abuse, domestic Violence etc. But the DSS would require copies of injunction letter etc