Yep, I agree with ausgirl on the soiled clothes issues. I'd take out the part where soiled clothing are put into children's bags as they aren't (or shouldn't be), and add in a part that says something like "in line with policies, I will provide an airtight container/bucket to put used nappies in, as is the guidelines for soiled clothing" (or something like that lol, my brain isn't fully engaged right now!). It sounds like their issue is with putting dirty nappies back into a bag, which I can appreciate they probably aren't allowed to do. I guess if you and some other parents who use cloth pooled money and bought one of those storage containers to keep at the centre, and then each provided a wetbag, staff could put dirty nappies in the wetbag into the container, as they do with soiled clothing. It's not more work since they have to change dirty nappies and put them in a nappy sack and then the bin anyway, so its just changing the 'bin' step to 'container'....

Hope you can change their mind. Disposables for CC could get really expensive especially since you're already outlayed the money into cloth.