This is exactly how it reads to me too.
They sound very different to OP. She's not interested in the way they do things. I love a four course Easter lunch all cooked for me and my family. (And in fact we were, 8 of us.) We used the correct cutlery too. I'm not sure what all the gasps about stuffiness for using the right fork are about. It's literally picking a fork up.
Our DTwins are 4, and asked to get down after each course. DH and I told them no, we wait for our meal to finish, we distracted them, people chatted to them, we made things out of the napkins, and they sat. It's less relaxing adult conversation for us, and more keeping them engaged, but this will ease each year as they mature.
However, a meal this time last year? No chance. So...we hosted at ours, every single time. Every Easter, mother's day, Christmas, whatever it was. For 3 and a half years. DTwins would not sit nicely at any table. So we didn't ruin other people's expensive restaurant meals by taking them somewhere we knew they didn't have the table manners for, and we did the entertaining here, so if they were being grouchy 18mth olds, or shouty two year olds, we could deal with it/put one to bed/one of us could disappear off with them, and we weren't affecting someone else trying to host.
My DC are far from perfect. I don't expect them to be. I think it's a real sad state of affairs though with a basic expectation such as table manners, that to so many, the very concept of table manners is seemingly lambasted with silly comments like "oh well sorry my kids aren't all perfect like yours". How low is the parenting bar for the very basics like table manners to be "perfect." FFS.
I think the hosts fall into the camp of having a basic expectation of table manners (certainly of adult OP and DH) and OP falls into the camp of thinking it's preposterous any of her family shouldn't be allowed to leave the table halfway through a main course, all go and sit in the garden, and return for pudding to be served to them, whilst everyone else sits at the table eating the meal that has been prepared for them.
I think as PP has picked up on, this will likely not be the only difference between how the hosts conduct themselves and how OP conducts herself, and it's come to a bit of a head. The thing that did it, I suspect, was both adults leaving their food, so four plates were left unfinished because both parents, went out to watch their children (one more than old enough to sit at a table) play, in the middle of a high effort home cooked meal. It's very rude of the hosts to call her up and highlight this though. It didn't need highlighting, everyone there had eyes.
OP and them are clearly a mismatch. She shouldn't go back, but not because they are arseholes, their expectations were not unreasonable, certainly of the adults. But because OP genuinely can't see the issue, and they can't comprehend how she can't see this. Just raised very differently to each other, and it's really incompatible, and it's likely to be a "thing" now it's been called.