My oldest son didn't like veggies either at that age. In fact, he's 6 now, and still doesn't. He doesn't like the texture of cooked veggies, but he does like raw vegetables. He'll eat lettuce, carrots, red / orangs / yellow /green bell peppers, cucumbers, celery. Red bell peppers are his favorites. He likes them when they are raw and cold much like fruit is. My son doesn't like dressing either, but will eat them with croutons. You could try different salad dressings for dipping. Since he won't eat the cooked veggies at the table with dinner, I'll put a small pile of raw veggies on his plate as his serving. This also helps with his desire to want to snack while dinner is being cooked. Now, he'll munch on those while dinner is being prepared because that's when he's hungriest and then it's not a dinner time battle. Tupperware makes some great containers to keep sliced veggies last a while. As soon as I buy the veggies, I chop them up and store them in fridge smart containers so they are easy to pull out and I don't have to spend time chopping veggies at every meal.
My 3 year old is better about veggies, but his favorite is corn on the cob. He'll gnaw on that at dinner time. That's a good one to try. You can buy those little handles that stick in the end for less than a $1 at Walmart.
As for MDO, I wouldn't pull her out. My oldest son went to a babysitter when he was young and got tons of colds as an infant, so when he started pre-K at age 3, he never got sick. My youngest, however, has been home with me until he turned 2, so he's gotten his colds now. I think it's good for them as it builds their immune system. If she's getting them a lot, could it be allergies? My son's get hayfever time to time like I do, and the symptoms are similar to a cold.