It's pretty much how your mom did it here.
We eat together as a family at the table. No electronics, no TV, no phones, etc. They have to try one bite of everything I served, and then they can have more of just the potatoes or whatever if they choose. I don't really tell them what to drink, but I don't buy soda, so there aren't that many options. It's milk, hot tea or juice.
I don't make multiple meals unless I'm making something especially horrifying for me and dh.