I don't think you can "teach" a kid what to eat. You offer foods, and let them choose what they want. It's very important for a child's development to be able to choose what foods he wants to eat. Obviously, you restrict the choice in that you get to decide which choices to offer them.
My kid is 1 & 1/2 and eats many various fruits and veggies. I have never, ever forced him to eat, or threatened him of anything if he didn't eat something. He eats broccoli, peas, leeks, turnip, potatoes, beets, kale, cauliflower, tomatoes, bell peppers, fennel, mushrooms, onions, garlic, shallots, cucumber, peaches, prunes, strawberries, raspberries, meyer lemons, oranges, mandarines, pear, apple, dates, dried apricots, pineapple, blueberries, etc, etc...
To me it's not surprising he eats all that, it's just what we eat in our house, what we have in our backyard, what he sees us eat on a daily basis. Note that I'm not saying that any day of the week, I can sit him down in front of a plate full of any of those and have him eat it. I'm just saying he's eaten all of that in his first 1 & 1/2 year of life. A lot of time he doesn't want it, and that's fine, he's got other choices. For example tonight, we were eating chicken adobo with white rice. But my kid first had whole wheat macaronis and cheese, fresh pea puree, and "pancakes" made with fava and chickpea flour, with sweated shitake. Then he sat with us and had chicken adobo. Then he ate a frozen strawberry kefir popsicle.
Well he's still really young obviously, but he hasn't been introduced to junk food yet. I know he'll have it later, and that's fine, but there's a time for everything. Right now he's developing his little palate, and I'm trying to expose him to as many varieties of fresh, healthful foodstuff.
I believe the toddler years are important as that's when the palate develops. If all he eats is processed foods, he's going to develop a taste for the flavorizers used in those foods, and later in life he will search for the same flavors in junk food.
Your sister shouldn't force them to eat anything. But she can't expect her kids to eat stuff she doesn't eat. If she wants to change her kid's habits, she has to start with the habits of the whole family. I also believe you have to make kids involved. My kid comes with us to the farmer's market, and he wants to taste every sample, touch every fruit, every vegetable, and we play games to identify the easy ones, and I tell him their names, etc. Once home, I have him "help" me prepare stuff (he'll hold the spoon for about 1mn in the pot without stirring, or I give him the peas one by one as I shell them, for him to put in the steamer basket... etc).
Since you're on this forum I'm assuming you love to cook. Maybe it could be your role, as the Uncle, to once in a while have your niece and nephew over, teach them how to shop at a market, show them how to cook, and get them excited about fresh healthful food again.
Best of luck to you, to your sister, and to the little ones.