I know it's hard, but you have to put your foot down. Boundaries are important. Everyone should be responsible for cleaning up their own mess. Or, if you cook someone else has to do the dishes. Stuff like that. We do the cooking/dishes thing here most of the time.
I would be a horrible mom. I would take my kids dishes out of the sink,put them in a bag or something, go to their room with them. Tell them they can't use another plate until those are clean.
Jeez I really would be a mean mom.