I remember the tactic my parents used. My sister and I had to have TWO BITES of everything on the plate. Some nights we were just not hungry or whatever. Two bites of the vegetables, meat, etc. and we could be done. Nothing special was ever made if we didn't 'like' the dinner (very rare, my sister and I were not picky eaters!). The only time we'd balk as little kids was if something very alien was served. This was more my sister though, especially when we moved to Japan. I embraced living in Japan, which meant exposure to new and awesome foods, but she didn't like it so much.
Be strong! I hope your 9 year old gets out of that belief that vegetables are going to kill her. I have read that children's taste of bitter is much stronger than an adults, so often a poorly cooked vegetable (not bashing your cooking stills!) can leave them with a bad memory of that bitter tasting vegetable. What was a defense mechanism against eating poisonous (and often very bitter) plants when we were hunter/gatherers has turned into a nightmare for parents trying to get vegetables into their kids!
Be strong! I hope your 9 year old gets out of that belief that vegetables are going to kill her. I have read that children's taste of bitter is much stronger than an adults, so often a poorly cooked vegetable (not bashing your cooking stills!) can leave them with a bad memory of that bitter tasting vegetable. What was a defense mechanism against eating poisonous (and often very bitter) plants when we were hunter/gatherers has turned into a nightmare for parents trying to get vegetables into their kids!