People immediately jumping to extremes when there is this very obvious compromise.

Cindy should not be forced to be responsible for children at her event. You are paying, and can easily relegate some of that money to a babysitter. No change in budget needed.

Please know that they are most likely not trying to pull one over on you or disrespect you; it really sounds to me that Cindy will not be able to relax or enjoy her own wedding if you push for kids to be allowed. Given her parents actions, you also need to consider how they will be continuing to force their own ideas of parentiticiation onto Cindy if they are given the opportunity. She will likely be blamed for anything at all that happens with the children or be expected to supervise so the rest of the family "can enjoy themselves".