I don’t think that logic and the CSA belong in the same sentence.
I speak only as someone that has listened to tails of woe from friends.
I would ask why you need to tell them anything as I can’t see what would change as she would be spending the same time at the different houses.
I suppose you would have to continue to pay £180 but if her Mum pays you £360 you’d be quits?
I’ve perhaps misunderstood.