This seems to be a very simplistic (and maybe a bit selfish) piece of advice, but you may be able to take the basics of it and customize it to your own situation.
I decided to lose weight last summer, so I plan the family meals and snacks around MY eating needs - that is to be healthy (which should be for the entire family regardless) and to lose weight. I have actually focused on the eating healthy, not the losing weight.
Like your kids, portions have always been my downfall, so I now cook only what is required for the meal...no seconds, no leftovers. The snack foods and desserts in the house are only the things that fit into the healthy eating plan - low fat, low calorie, low points. Period. One thing that I have also discovered are the flavored waters (fruit flavors), that are artificially sweetened. I use these to satisfy my sweet tooth and find, through drinking them as my water quota, I don't have cravings for sweet things.
Hubby has always been on the skinny side, but has been developing a small tummy over the past few years. Not anything noticeable, but he has had to buy a 34 waist instead of a 32.
In the past 9 months he has dropped the little tummy without really even realizing that he has been "dieting," too.
Anyway, my suggestion is to put your entire family on a healthy eating plan and don't discuss it with them, just serve it. Your children may lose weight slowly if they don't realize that they are actually following a plan. They may not lose as quickly as if they were following WW, because they won't be completely true to the plan, but it will be better than nothing.
Hope this helps. I know how important it is for our children to grow up as healthy individuals. As mother, I guess we always worry about them.