I was born in 1960. Growing up, all us kids ate dinner with Mom and Dad every night, eating the same food.
At big family get-togethers, there was usually a kids' table, but mostly because Dad was one of 6 kids. My two grandparents, their six children and their children's six spouses pretty much filled up the dining room. So the kids would be put at folding tables on the front porch in good weather (with the windows to the dining room open so the parents could hear what was going on), and in the front hall in the winter.
We *loved* the kids' table. No parents to supervise us. A good chance to talk with our cousins that we didn't see very often. The older kids were not babysitters, but they did try to keep things under control so that a parent would not feel the need to come out and investigate what was going on and spoil all our fun.
The really small children, babies and those under maybe 3 or 4, ate with the parents.
We all had the same food, unless there was something that Grandma felt the kids would not like. So the adults might get spinach, but the kids would get green beans. Although if a kid had asked for spinach, I'm sure they would have gotten some.
But then, Grandma was very enlightened for her day. If you (a child) didn't eat your whole dinner, at home with your parents you would not get dessert. But Grandma felt that the milk and eggs in her homemade puddings and ice cream were nutritious, so if you didn't eat all your vegetables, then you *needed* that ice cream to help keep up your strength.
As we all got older and more and more babies were born and the older cousins started getting married, the table in the dining room was for those who needed to sit at a table to eat--moms with babies, aunts with arthritis, that sort of thing. The rest of us scattered over the first floor--some sitting on the stairs, some in the library, some in the kitchen, some outdoors if the weather was good. (There could easily be 65-75 people at a family gathering.) So there was no official movement from kids' table to grownups' table, as the entire system changed.