How long have you been trying to improve your children's diet? If you have obstacles (like school, grandparents, HUSBAND) it will take longer than you might hope.
If you're dealing with children who immediately announce they don't like something, please try a new deal - they must take three normal bites of a new food/dish on THREE separate occasions before rejecting it completely. Then, after each introduction, ask them for specific things they don't like. Often, if it is texture, you can prepare it a different way. If it is taste AND texture, the three times will help you know if they just aren't used to it, or if they really hate it.
You may have to take this more slowly try introducing simple substitutions for some foods and slowly eliminating them. If their Dad isn't supportive of any of what you're doing, they'll throw "but Dad doesn't have to eat it" at you, and frankly, that's a tough objection to remove.
Fat in and of itself will NOT change your children's taste buds from the refined foods to other things. Remember that one missed meal (if they don't like it, and have done their three bites agreement), won't cause death by starvation.
Get them involved in the shopping AND preparation of food. First, they'll understand where food comes from and the commitment it takes to prepare it for consumption. Second, they'll learn to cook. Third, they may come to dislike the chemicals infused in food and reject it for freshly made. Fourth, if you're eating out a LOT, stop. That alone will help accelerate your efforts.
Lastly, subscribe to the 100 days of real food blog. This mother of two girls, aged 3 and 5 chronicles her attempts to improve. It's been over 75 days, and her kids don't clamor for refined unhealthy foods anymore. Let me warn you -- this was a HUGE task on her behalf, and her chronicles might help your efforts. Check out her blog here: http://www.100daysofrealfood.com/. She has a companion site for recipes called Food Illusion. That link is on her 100 days blog.
Good luck! And be patient. You WILL prevail!