In her website for Deceptively Delicious, Seinfeld says that her oldest child is "turning seven next month", which means that she gave up on feeding her children vegetables when they were maybe 3 and 5 years old. That is awfully early to be giving up. Most pre-schoolers don't like strong flavors like spinach and beets, so if that is what she was trying to feed her "picky eaters", no wonder she had trouble getting them to eat. Rather than try to feed toddlers and pre-schoolers a "full" range of vegetables, aim for a variety of colors and start with things they will like, such as carrots or mashed yams for oranges, cherry tomatoes for red, romaine lettuce or green beans for greens; jicama (a starchy white-fleshed root) is great for kids, because it is almost sweet, is eaten raw, and can be cut into sticks to eat with fingers. Fill in with fruits, which come in all colors of the rainbow and are almost universally liked by kids; puree them in a smoothie with yogurt, and you can get a whole day's worth of healthy servings into them at once. Strong flavors, like beets, spinach, brussel sprouts, even broccoli, should wait until the kids are a little older.
Scientists who study these things are now saying that a new food has to be introduced up to 10 times before a child will actually start eating it regularly. So start small, think like a kid, and be patient. Finger foods are always better than fork foods until kids are well into elementary school, so cut up yellow, red, and orange bell peppers into strips and serve them raw, maybe with ranch dressing. Give kids small amounts of raw broccoli, in small "trees", to eat as finger food with a dip; don't cook it and bring out its stronger flavors until kids are older and used to broccoli (and then cook only lightly or you ruin it). Do a whole platter of finger foods with dip and let them choose what to eat. Try an artichoke with lemon butter; the whole process of tearing the artichoke apart and eating something so improbable tends to intrigue kids (at least if the adults at the table are enthusiastic). Serve a mango/onion salsa on grilled beef. Add tomatoes or some spring spinach to tacos. Make spaghetti squash with butter or spaghetti sauce. Try a mild hummus (made with chickpeas) and crackers. Play with vegetables, have some fun with them - they don't have to be so serious.
Finally, when kids are maybe 7 or 8 (depending on how the adults in the house eat), start feeding them small amounts of the stronger vegetables such as large-leaf spinach, mushrooms, beets, or brussel sprouts, preferably mixed into something else that they will like. My family (including me) learned to eat beets when I started dicing them fine and putting them in a salad with grated carrots, hearts of palm, and plenty of vinegar; the early-season beets are milder than the dark red fall beets. Sautee some mushrooms in lots of butter and serve it with steak. There are some people who are super-tasters, and they still won't like the stronger vegetables no matter how often they try them, but there are lots of ways around the strong flavors that are still healthy; if they don't like broccoli, serve lettuce. Rather than fixing on any one vegetable as critical, serve your child a wide variety of vegetables in a range of colors and find out which ones they like; as long as they cover the rainbow, they will be healthy.