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!