They raise some points that need to be responded to I think -

Yes, cloth nappies leak at times, but so do sposies. Leaks are prevented by regular changing so the general way cloth nappies would leak is if the babies aren't changed regularly enough. I think it could be asserted that they are NOT changed regularly enough if your DD is coming home with nappy rash even in sposies.

So we have gathered that all nappies leak from time to time - that's why you provide a clean change of clothes. If all nappies leak from time to time and babies need their clothes changed then dirty, wet clothes need to be stored in the babies bags all day until home time. How is this different from storing a nappy in a proper, sealed wet bag?

Many babies have reactions to sposies (especially cheap ones that I presume the centre uses for cost reduction reasons) so what is their policy on how to deal with children who have reactions to disposable nappies? If they don't accept children into care who can't use disposable nappies then that is discrimination. What is their policy around that?

I would be contacting the other clothie users and combining forces to put together a response. Is this a private centre or a community centre? If it is a community or council centre then lobby your councillor as well.