I think their are a lot of cultural issues associated with meals and that culture varies hugely from family to family, and when it feels like it's going wrong it can get us at quite a instinctive level.
So my ILs have an everything on the table and pile it high approach, whereas my family carve and serve at the head of the table, giving each person a reasonable serving with the expectation of second helpings.
Personally I find the ILs approach really quite painful because to me it seems really gluttonous (dig in and don't think about anyone else) whereas dh thinks that my parents are parsimonious (counting the potatoes).
Really they are just very different approaches to meals, for my family meals are primarily about being together and talking. The food is always delicious and my mother aims for it to be 'just enough' because she hates waste (a long term effect of rationing). For my ILs meals are much more a time to eat and drink (the drinking being the key part really) so there is no incentive to stretch it out and the important thing is that it is seen to be very generous (a totally different response to rationing). At my ILs leaving uneaten food on my plate is great - there's so much food I've not been able to eat it all, whereas for my parents (and me) you finish your plate, so if you've left food it's because you don't like the food (and are so rude you've not eaten it anyway - my mother is a bit of a food nazi)
I think the OP is experiencing a similar clash of cultures, her guests almost certainly don't mean to be rude, but they are behaving in a way that makes the OP very unhappy. However she's not letting them know this because that would probably feel rude to her (although it might be fine if her ILs are making jocular comments to make them back).
If I were her I'd put the vegetables and potatoes on the table, but split so there are serving dishes near both the ILS and the children and serve the meat at the table (if carving) or bring the plates from the kitchen with generous portions of meat for all (as you know the ILs will eat lots and you also know how much your children would like). If the children are small I'd give them servings of everything in the kitchen before you put them out on the table. It doesn't have to be slow if you have the children in a row, serve them and get them to put their plates on the table and then carry through all the dishes for the table.