A lot of the time kids or adults are hungry on a diet because they are eating food that is metabolised too quickly.  If you eat high carbs on a low calorie diet and the fat level is cut very low, then you always seem to be hungrier for some reason.  generally those on a moderate carb diet with a higher fat level can lose weight but eat more and feel much more satisfied.    It’s a temptation to lower the fat in food but fat and protein slows the digestion of food right down and satietes you.  It is also absorbed much more slowly into the blood and you don’t get the insulin levels and blood sugar rising too high and then dropping dramatically.  It may be good for your children if you could concentrate on doing a few things such as cutting simple carbs and starch right back (don’t add table sugar to anything they eat for now) but raising their fat content in the food and the amount of protein they are getting.  

Good Foods

Complex Carbs - Veggies and Fruit (limit fruit or two pieces a day at first and eat the low glycemic ones.)  Try not to eat dry fruit for the time being as it’s high in sugar.  

Reduce saturated fat - Trim it off all meat and have them drink reduced fat dairy products.  Allow stews and soups to cool and skim it off the top and then reheat.

Raise Healthy Fats Instead - Those being the types in nuts and seeds and use olive oil for cooking.  Fish oil is good too--I take capsules mrning and night.  By replacing saturated with these typoes of fats, your making sure they are getting the healthier types of fat and they are getting the benefits of feeling less hungry.

Let them snack on low fat cheese sticks, nuts or fruit instead of candy and potato chips or cookies.    Even when they reduce the fat in a packet of chippies, they are still starchy and high in simple carbs and this type of snack will not help someone wishing to lose weight.  They are just going to be hungry soon after them.

To slow the digestion of food down even more take psyllium/metamucil about 15 minutes before eating.  It delays the passage of food through the gut and they will be satieted for longer.  

If your kids like desserts, then you can make them a lot of desserts out of eggs and ricotta cheese and splenda which are low glycemic and filling whilst they are losing weight.  Don’t make any base for quiches, tarts etc.  Just make the toppings using splenda or stevia. 

I add x2 heaped tsp unsweetened cocoa to 125 grams of ricotta cheese and a tsp splenda, tsp vanilla essence and sprinkle some chopped nuts and about x6 chocolate sprinkles on and even with the chocolate on it it is low glycemic and filling after a dinner.  If you want to make that dessert higher in protein and make it go a lot further, use whey protein powder or soy powder - flavorless and mix it into a smooth paste using some skimmed milk or water and stir that in also.  This I like making when I feel hungry after dinner and craving something sweet.

I think it may have to involve you and partner eating that way and getting rid of ALL stuff out of the house.  If they are hungry they will then eat what is on offer. 

I would cut starchy carbs down to x2 portions a day.  A portion is:

x1 slice of wholegrain bread

1/2 cup "cooked" oats

1/2 cup "cooked" brown rice.

1/2 cup "cooked" wholemeal pasta

Choose brown as opposed to white as it is digested slower.  Steam brown rice for longer and it will go as soft as white rice but be better for them anyway.

It doesn’t cost much to eat this way either.  There are also weight watchers jello which is something you could use with a thin layer of cream on top and a low sugar custard underneath the cream - trifle.  That is low glycemic and will be filling after any dinner.  The fat in the cream will satiete them.  I think kids especially are exposed to a lot of food that is high in sugar these days and it’s only that in combi with high fat-especially trans fat, that is a problem.  Use margerine made from olive oil.

Make mini quiches:

spray the tin with olive oil and put wholegrain bread in there as a base and then add your quiche filling - egg, skimmed milk, a little salt and pepper and veggies of your choice.  We use mushrooms, tomatoes and broccoli cut into very small pieces.  They can be frozen or stuck in the fridge and it is as easy to grab one of those out and eat it as it is to grab a cookie.  More healthy.  ;)