I think you handled the initial situation fine, and I would just completely ignore Uncle's email. There are lots of ways one could phrase a polite reply, but I don't see the point--it seems clear to me he's not going to be persuaded to change his mind, and since everyone involved is an adult presumably capable of speaking up for themselves at the time, I don't think you need to do anything different in the future.
The only thing I might do is forward Uncle's email to, say, my parents and whoever was the "host" of the gathering--grandparents, I think? Not to cause drama, but because in the future I would like those who support me to do so out loud; and also to double-check with the hosts that they didn't feel I'd overstepped. The latter would be my only real etiquette concern in this situation--you can't use the "my house, my rules" stance, so since there was an objection after the fact, I would like to make sure that the actual hosts are overtly okay with what I did (and plan to do in the future).
As for the littles, I know how easy it can be to get complacent about what one usually does in a situation, so I don't necessarily blame them for not figuring out on their own what they ought to do. Once it was mentioned, though, they should have immediately and cheerfully joined in, for both meals. If they thought about it more they would realize the tradition really was that THEIR generation cleans up, and now their turn has come up.
I gotta admit, I hate washing dishes and I've never offered nor been asked to do so at family gatherings. It seems to be mostly the host/owner of the house (male and/or female) who handles that, and possibly their older children. And my dad, who seems to really like washing dishes.
If someone suddenly, out of the blue, asked me to help, I hope I would do so graciously, but I wouldn't like it--I would much rather be expected/asked to help because I was part of X generation who has always done this (as happened in the OP), as opposed to because I was in the wrong place at the wrong time, looked like I was bored, am female, etc.. In other words I am happy to help if it is the tradition that all people in group X help (except not divided by gender lines) but I don't want to be "targeted" individually because I am polite enough to agree while others scoot away.