*Sorry but you really need to teach your children table manners. It doesn't matter if you were not taught about any of this. You really should teach your children, if only so they will not suffer these problems later on in their lives.
I am not talking about 5 different knives and forks for each plate, but at the very least they must eat with knife (right hand) and fork (left hand), wait until everyone has their food to start eating, chew with closed mouth, and place knife & fork appropriately when they are finished. *
I'm not sure the left and right hand thing matters. We always laid the table for the evening meal at home, and you always knew when it was my sister's turn at laying the table, because the knives and forks were the wrong way round, but it takes all of about 2 seconds to swap them round for the rest of us right-handers, so it's hardly a big deal. And I think if someone's eating competently with cutlery, you're going to notice that far less than someone being forced to eat with the knife in the right hand when they're left-handed and not used to it, as it will make them clumsy with it.
Having said that, though I'm right handed, from time to time, I've found myself using cutlery the other way round without much difficulty, so I don't suppose it's that difficult to learn to use them in a right-handed manner when you're not - it probably all depends how far along either end of the spectrum you are between left and right handedness and ambidextrousness (not sure if that's quite the adjective for being ambidextrous, ambidexerity maybe? But whatever.)
Though my parents had their faults, one of the things we were very lucky with was that we grew up mixing with people from all sorts of backgrounds, so I knew people who went to Eton as well as those in Council houses with very little money at all. What it's meant is that I know you get lovely people in all strata of society, and you also get snobs at all levels. The ones worth sticking with are the ones who are interested in people for themselves, and not how they do everything. I find it interesting that people do do things in all sorts of different ways, but I'm mostly not going to look down on anyone for it.