Picky toddlers are like the rest of us - they need nutrition, and that's a lot more than just vitamins. They need the fiber, the protein, the healthy fats, the minerals, the trace elements, and more. The AMA released a paper in 2002 indicating that everyone, even those who "eat right", need to supplement because the American diet and even fresh food crops are deficient. Is it worse for picky eaters and those who live on fast food? Sure. But the AMA reached the conclusion, after a great deal of study, that nobody's getting everything they need, which is why we have a variety of health crises on our hands. Panels of physicians and nutrition experts have agreed - we'd need to eat thousands of more calories a day to get what our bodies really need to flourish.
Now, does your pediatrician agree with that or not? I don't know. There are plenty of doctors who don't feel they know much at all, since they never take nutrition courses in medical school. Lots of them think standard multivitamin complexes, which just have a handful of vitamins and minerals, are basically "expensive urine" because there's not enough in them (in terms of the number of nutrients, not the milligrams of the few) to get any decent absorption - so they are eliminated in the urine without being utilized by the body. There are hardly any who still believe that you should take individual nutrients even if blood tests show you are "low" in that - that's just not how the body utilizes nutrition. There are still a few people out there recommending that someone take extra Vitamin D if they are low in it or calcium if that shows up low, but most recognize that it does very little good (and often harm) to supplement that way.
I think with kids, you have some options. You cannot turn meal time into a battle ground. It's important to accept that you control only what goes into the shopping cart and onto the table. The child controls what goes into her stomach. I do believe there's value to hiding ingredients in other things, and I was a master at it with my child. I hid spinach in hamburgers, tofu in Italian foods and yogurt, and even broccoli in pancakes. Yes really! But having moved from women's health education into food science education, I've learned much more about effective supplementation so I wouldn't make myself as crazy about the hidden veggies as I did then. However, I do think there's value to adding a little bit at a time to get them used to the taste of things, while supplementing (not with multivitamins but with a complete food that doesn't have the "keep out of the reach of children" warning labels). That way, they get the taste of the spinach and squash little by little mixed with their favorite foods, but they also get the nutrients in a highly digestible and absorbable supplement.
So I think it's all about balance. You take away the junk fillers if you have any - the sugary cereal, the processed crackers, the fruit roll ups and so on. You have healthy choices available, and you open your mind beyond what "standard" breakfast foods and lunch foods are. There's no reason a child can't have PB&J for breakfast - just use a low sugar PB, an all-fruit jelly without added sugar, and a whole wheat bread. PB on apple slices are good too. My son loved his starches, but even though we filled French toast and pancakes with power nutrients, he still had fruit as his "first half" and then the starches (which were filled with protein) as his "second half". You put a few things out in an appetizing way, with an array of colors. If you use a sectioned plate, fine. I've seen some people use an ice cube tray with little sections offering a mix of things (nuts, fruit, veggies, yogurt, cheese, cubed meats, and so on. If she puts food in her mouth and doesn't swallow, don't make a big deal of it. If she's not spitting it out, you can consider that the taste doesn't bother her so much as the texture - so you can think about serving that same food in another fashion (example: puree butternut squash and mix it with mac & cheese).
Switch to the whole wheat version of "white" pastas, brown vs. white rice, sweet potatoes vs. white ones (or mixed together). I do oven-fried potatoes vs. frozen French fries, make my own nuggets with chicken tenders and wheat germ and flax seed, and so on. Something like a whole wheat Triscuit is a better choice than many other crackers with additives. Plain popcorn made in a pot on the stove is better than microwave popcorn with chemicals (plus you can make a tiny amount). Even a piece of dark chocolate is better than a half a bag of Halloween candy.
When your daughter is "done eating" she can sit quietly with a book, or she can be excused from the table. Don't obsess about what she ate or didn't eat - just take the fight out of it. If she's filling her mouth up, ignore it. If she's ready to get down, just be cheerful about it and have her swallow or spit what's in her mouth (but don't make a value judgment about which one, just give her the trash bucket to spit out and walk away). Don't teach her to spit out on the plate, and I wouldn't do a lot of intervention about sweeping out the mouth myself.
Kids DO have to eat a lot of times during the day so have an array of snacks ready - that means cut up cheese cubes in the fridge, a cut apple (slice it like a tic-tac-toe board as you look down from the top and then bind it with a rubber band - it won't turn brown but it's already sliced and can even go in the car with you like that), a small dish of peanut butter or almond butter for dipping, matchstick carrots and other veggies with a little hummus for dipping, and so on. Mix it up but make sure there's an array of food groups and colors. Then let her choose from the day's available choices - usually 2 choices are good for that age, but have 2 more choices for the next snack. That gives her some control of the choices, but you are in charge of the overall available menu.
I wouldn't make her an entirely separate dinner, but I do think that things like a family salad bar or taco bar let a child choose from what's available and still have the image that she's eating what you're eating. If you can make food in fun shapes, there's nothing wrong with that now and then - cookie cutters for the sandwiches, mini-versions of adult samplings, and so on. But not all the time.