['My kids are so bad about bringing their dirty dishes to the sink and not rinsing them off.']
Aw man, kids can be SO lazy and don't like to do what they're supposed to. Have you tried a rewards system to get them to do what they have to, or are they too old for that?
My kids will bring their dirty dishes in and put them in the sink without washing them off. We don't have a dishwasher and I have to end up scrubbing those by hand. It drives me nuts.