Thing is, she's worse off regardless now.
Say she was getting £300 a month through private arrangement, even though Miss Grabby is entitled to nothing. Plus 2 lots of CB, say £150 a month. Plus, two lots of the UC child element, and critically if she rents, the amount due for a property to house 2 children.
She then gets more greedy and goes for CMS on both children, who she doesn't have to look after or pay for, for 6 months (!) of the year. (Fucketh me, the extra cash and spare time to earn I'd have if someone took my kids for 50% of the time!!). So for a snapshot of time, she gets her UC package, her double CB, and say £450 a month CMS for 2 kids. "Win."
The father rightly thinks "wtf" and challenges. Now he'll get the rights to the CB for one kid. Not any money. He'll pay that back. But OP? Ooooh....
Loses the CMS for one kid. So CMS now maybe back to the £300 per month. But now has to pay him CMS. Let's call that £100 per month. So she's £100 worse of in maintenance terms than pre-megagreed. Also loses the CB for one kid. Say £80 per month. Then she loses the child element of UC for that one child, is it about £290 a month? And then she loses the potential housing element of that child's extra bedroom requirement. Can be several more hundred. Although if same sex and similar ages etc they would be expected to share so this won't change.
Just going on the CMS to pay, plus loss of CB, plus loss of UC child element... Miss Greedy has done herself out of £470 a month.
Imagine, poor dot, she's going to have to work harder to earn and provide for her own children in her care for a whole 6mths a year.