Get in touch with the benfits maximisation team at the coucil and get them to help your cousin claim for child Benefit, WFTC , rent support etc.
As a kinship carer they may be avaiabe for discretionary payments from the council, it is to become compulsory in some areas of Scotland but is unlikely to reach foster care levels.
Be aware that by being assesd as a foster carer, they may fail and the kids wil be removed.
If your other cousin was in receipt of benefit for them, she'll still be getting it, so instead of moaning to the social,...get the money off her, after all they are her kids.