My son was a veggie hater. My daughter told him.broccoli.were.little trees. I let him dip carrots into anything. Then when in doubt I sneak gerber pureed squash into anything with tomato sauce or.mac and cheese. It tastes a little.different so I call it mommy magic. He.loves it. Jessica Seinfeld has a good.book out too called Deceptively Delicious. It is how to hide veggies with recipes.
My kids are pretty good about veggies. They are super meat eaters, though. I try to cook just enough of the stuff they get plenty that everyone gets a serving of it, and any left overs go into Daddy's lunch box. That way, if they're still hungry, they are taking seconds on veggies.
When my middle guy was a toddler he did not like lettuce. I swear I found a way to incorporate it into every dinner until he ate it. We had taco salad five times in two weeks. lol. He's great, now.
A favorite around here is green cheese lasagna. I mix around 20-30 oz thawed frozen fine chopped spinach with the 15oz of ricotta. No meat, just pasta sauce, oven ready noodles, green cheese(with an egg or two), and cheese. Last time I put mushrooms in it, too. My kids did protest a bit this last round, but only because they finally figured out the green wasn't food color.
I have a multi-pronged approach to feeding my twiblings veggies (they are 2 and 3)...
1) Education-We frequent the farmers market and let THEM pick their own veggies, they learn the difference between veggies and fruit, the names of different produce, and they get to know the people who produce our food. This way they feel excited about eating "their" selection that "farmer ty" grew for us! They also seem more inclined to sample veggie they helped grow. Last season we grew purple skinned tomatoes, and while they sometimes balk at store bought reds, they gobbled up the purple kind!
2) Crouching carrot, hidden cauliflower- Every meal, we offer veggies in plain view. Raw or cooked carrots, cauliflower, greens, whatever...these are frequently left only partially nibbled (or totally ignored in my sons case)...BUT I also add pureed or chopped veggies to pretty much everything, or make things that are veggies disguised as kid faves. Think Mac n' cheese with pureed squash, eggplant "nuggets", grated yellow zucchini in scrambled eggs. They always eat the hidden veggies at least.
3) Offer, don't force- I TOTALLY get that it gets frustrating to repeatedly offer veggies that get pushed aside, and they aren't cheap so it's especially irksome when they end up on the floor! However, having been forced to eat things as a child, I really believe repeated offering is the best strategy, not forcing.
GOOD LUCK LADIES! Lots of wonderful ideas, I enjoyed reading through them. May all our children eat veggies!
My DH on the other hand! The only veggies he would eat for years was green beans or corn. He's much better now. He actually tried a brussel sprout the other night. Only took 36 years! Said it wasn't too bad! Of course he didn't like steak when we got married, because the only way his mom ever cooked it was fried, until it was tougher than old shoe leather.
Anyway, I remember when I was a kid and my Mom wanted me to eat things I didn't like. I hated that. A lot of the time, it wasn't so much the taste as it was the texture.
For example, (not veg I know, I liked veggies), as a kid, potato salad and macaroni salad and cole slaw made me gag! Potato/macaroni salad, as a kid, I liked the the individual components, just not all mixed up! Slaw was just weird. The veggie I did not like as a kid was cooked peas. When you stick a fork in them and they squish out all over, could not stand the visual! Looked like an icky green worm!
One thing Mom tried to get me to eat, that I downright refused, and starved was headcheese. It's some gelatinous goo made from the leftovers after home butchering a pig.
Anyway, lots of great suggestions. Creativity, sneak it in, in casseroles and sauces. Ask them why, is it taste, texture, looks? (smooshy peas)
One thing I did when my boys were little and starting to teethe was give them frozen peas and carrots to snack on. I would just give them to them loose on the high chair tray, or sit them down with a small bowl. The cold felt good on the mouth, and they got to do some hand/eye/eating coordination in the process.
Thankfully, as we grow up our tastes do change, I like tater/macaroni salad now. I will eat slaw, but only my recipe.
Keep offering it, try at least one bite, be creative, have patience.
I read somewhere that putting sparkles on everything works a treat (pun intended!). I don't have kids but from my own experiences as a fussy eater, I had a select few that I would eat: peas and carrots. It wasn't until I left home and decided to be adventurous that I started eating a variety (my mother recently commented that she was shocked I was eating mushrooms!).
I can only suggest that you try finding vegetables that they like the flavour of, then try finding more with a similar taste. If they are fussy, it's going to be a battle of wills and you just need to be patient and persistent
We made sure the boys saw US eat vegetables all the time, and just set the platter on the table, after awhile, they served themselves some without being nagged to "eat it!"....but they were close to 5 yrs. old before they did that. As they grew, they tended to like salad better than anything cooked or steamed. When you think about it, vegetable non eating seems to be the norm for most kids, because, let's face it, the veggies aren't really the best tasting things in the world, unless you add fatty stuff to them. So you learn to compromise.........it's just the way it is. Nagging never worked on anyone, usually gets you the opposite result.
I wanted my son to be open to eating everything especially vegetables. So I made sure from the time he started eating solids to give him different veggies and fruits even if I have never had them before or even liked them. I also started trying baby lead weaning, which he just flourished with. When I started my diet I started trying new things with him. Now I got the exact opposite problem you have. He refuses to eat his meat and will insist on picking out and eating all his veggies. Lets just say there has been an increased frequency of diaper "blow outs". So now I only give him meat first. Once he has eaten enough to satisfy me he gets his veggies. I wont even let him see them or he will cry and throw his meat on the floor. He is usually hungry so when he thinks all he is getting is what is on his plate he'll eat his meat. All I can suggest is give him his veggies first as others suggested. Now that I think of it I have found protein alternatives that I mix into his veggies to help make sure he gets enough (ex. Quinoa). Perhaps as other suggest you can mix in veggies so he can't tell they are there or add other alternatives with similar nutrients into his food.
As someone said above, I also serve my daughter in "courses" and we always start out with veggies. She is 5, and getting pickier by the day, lol. The ones she likes best are the "fun" ones that are finger food, like baby carrots and, her all-time favorite, a bowl of cherry or grape tomatoes and some black olives throw in. She will then put a black olive on the end of each of her fingers. I realize this is not teaching her that playing with one's food is not appropriate, but at least she's eating them.
Out of nowhere last week I devised a five page chart of veggies with a column for a checkmark, a picture of a veggie, the veggie name, and a smiley face without a mouth. My just turned six year old is having a blast picking which vegetable to try next, and how to rate it (with a smile, straight face, or frown).
She has always been a good eater, but I wanted to advance past her regular vegetables: zucchini, summer squash, cauliflower, broccoli, green peppers, carrots, corn, and tomatoes. I posted this earlier, but I naturally mix vegetables into nearly every dish I make.
This week she ate onions, peppers, and okra and told me it was delicious (okra got a special smiley) and tonight we have mushrooms, tofu - not on the list but a newbie for her, scallion, and snow peas.
Tomorrow we're having braised bok choy. She's just excited to have a part in planning and picking exactly what to try next, and I'm not stopping her! Her next choice is acorn squash, but I told her she needs to wait for the weather to get colder
They also seem more inclined to sample veggie they helped grow. Last season we grew purple skinned tomatoes, and while they sometimes balk at store bought reds, they gobbled up the purple kind! 
