Lea-
Well, on the bright side they like apples and carrots

Do they like any kind of sauces or condiments on to dip the nuggets, pour over the steak or hot dogs?
My mom used to "hide" fruit and veggies in almost everything that we ate. She would steam and puree veggies and hide them in pasta sauces (not necessarily red sauces as I see your kids are into plain pasta), salad dressings, ketch-up, homemade pasta itself, mac and cheese, breads, pizza crusts, muffins---you name it, lol.
You could try this with the ground meat, very finely chopped zucchini, ground bean paste, tomato paste or mushrooms would probably blend right in. Start with a small amount and then get a little more daring. Also, if you can get the meat in a ww tortilla wrap maybe you could sneak in even more.
I really like Christine's recipe b/c it's easier to hide things in baked pasta dishes.
Also, sugar snap peas are VERY sweet (more so than carrots) and you might be able to get a few down them.
When my brother and I were little we'd eat frozen peas (still frozen), but not defrosted. And other frozen fruit, blueberries, grapes, cherries, etc. make a nice treat, especially if you give a flavored yogurt dip. I've gotten quite a few of my younger cousins to down quite a bit of fruit this way :7
HTH,
Mattea