Its very wrong of them to point blank refuse to use them!
However, and I dont want to get shot for this
as childcarer it is very hard/difficult if a parent asks you to do something you dont understand. I would be looking at where the problem is, you say she has moved to a different room, so I'm guessing its someone else doing the nappy changes? Maybe this person needs training in changing cloth, you could offer to show them? Does she have lots of leakages/full changes of clothes situations that are upsetting them? Maybe you could add extra boosting to make nappies last longer/ tell them to change nappies sooner? Do you use paper liners, maybe this would help them?
Personally I wouldn't be pleased if someone sent a child to me in pockets, I've just never been able to get on with them and always used fitteds. I would give them a go though and even offer to use mine if needed! Maybe the nappies which work for you, dont work for them? We all have our preffereances.
I hope the situation can be resolved.