I've been a vegetarian since I was about 17, so I don't qualify for the first portion of your post.
However, I do have a 9 year old son that eats meat. I've never tried to make him a vegetarian because I feel that is a personal choice. He will make that choice when he is old enough if that's what he wants to do. He's been eating meat all his life. He likes vegetarian dishes and he also likes "fake" meat made by Boca or Morningstar Farms. He loves the corn dogs, the hot dogs, chick patties, and the "ground beef" from Morningstar Farms. He also likes the new "chicken strips" and "beef strips" made by them. I make fajitas out of them. He doesn't really go for the burgers though.
I rarely serve him meat at home, but we do dine out once or twice a week. He usually orders chicken strips or things like fish or shrimp. He is not a big fan of beef, but that just comes naturally to him. He also eats meat at his grandmother's house.
I would suggest serving your meat eaters things like chicken breasts with the vegetarian dishes you eat. Eating veggie is healthier. Also, try the "fake" meats. They're so versatile. The "ground beef" can be made into tacos with a packet of taco mix. It can also be made into meatloaf. Just cook it on the stovetop and let it cool off a little. Mix with an egg or two and italian bread crumbs. Press into a loaf pan (the kind used for bread) and top with a mixture of ketchup and brown sugar. It's yummy. You can also add some sauteed onion to change it up a bit.
The new "chicken strips" by Morningstar Farms are great in the Taco Bell Gordita kit you get from the store. Just cook them in a pan and then add the packet and water per the directions on the box. You don't have to put the creamy sauce on your gordita. Just add salsa, lettuce, light sour cream and tomato. It's a quick dinner.
Here's another recipe your family might like. You take the fake ground beef and cook it. Mix in one regular sized can of mushroom soup without the water (can be lower fat/lower sodium version) and one can of sliced mushrooms. Make about 6 servings of instant mashed potatoes. When those are done, stir in a small container of light sour cream. Put the meat mixture along the bottom of a baking dish. Spread the potatoes on top of the "meat". Sprinkle with shredded cheddar cheese (if you are on a diet go lightly with the cheese). Pop in the oven at 350 and bake for about 15 minutes. All the ingredients are already cooked so you are really just heating it through and melting the cheese. I call it "Shepherd's Pie" even though it is not the traditional way of preparing it. That's my son's favorite recipe. I've developed lots of crafty recipes over the years.
