Vicky,
I don't know how old your children are, so I'm working a little bit in the dark.
One of the benefits of being a parent (or parents) is unlimited executive authority. Your kids don't get a vote. It's certainly useful to solicit their opinions on certain issues, but on things that you feel strongly about you are under no such obligation. If you don't want your son eating ice cream cones, you can eliminate them from your shopping trips. If you don't want your son eating three ice cream cones, you can say "no" after one. Or after two.
Here's where the age factors in. It' probably not reasonable to expect a five-year-old or even a ten-year-old to make healthy eating decisions. There are exceptions, of course, but your average kid of that age will usually choose the Kool-Aid over the celery sticks. Children need parental guidance in all facets of their life, from ethics and morality to food and fitness. There will be plenty of opportunity for your children to explore their individuality (clothes that annoy you, music that drives you nuts, and friends you can't stand

). Their nutrition probably shouldn't be one of these areas.
In your home, don't feel guilty about making dietary choices for your kids and then enforcing it by rule of law.
Good luck!