Please could you share with me what vegetables your children like and which they will eat with much encouragement bribery?
My children are veggie but they aren't keen on vegetables! I was the same to be fair but now enjoy far more.
Middle one will eat:
Carrots,
Cucumber
Corn on the cob,
Cauliflower,
Tomato based pasta sauce,
Celery in homemade soup,
Any veg blended in soup
Eldest is fairly easy going and will eat most things.
Little one copies big sister's err I can't stand that! But will eat:
carrots,
Cucumber,
celery in soup,
anything blended in soup,
Tomato based pasta sauce,
and will pick at salad leaves
None of them will touch peppers, courgettes, mushrooms or onions. But I can roast peppers, onion and courgettes and blend them into homemade pasta sauce 
I'm trying to get us all eating healthier and want to do more homemade meals but am struggling with their limited likes.
They don't like melted cheese so cauliflower and broccoli cheese aren't an option. I despair.
They've recently decided they'll tolerate curry with various things they like in it.
No one likes green beans. Horrible squeaky things.
Potatoes are fine, but LO not keen although not a vegetable in terms of 5 a day or 10 a day or whatever. Any a day is a bonus.
I'm hoping your list of likes will inspire me.