Hi Sam. My kids are 12 and 16, so the damage is done in this house, and it's me that did it, the treats in the house were always mine. Master 12 talks about going no sugar, but he asks for soft drink ALL the time, he's used to it. Miss 16 is overweight and just won't control what she eats, no matter what we try.
My suggestions:
First of all, I'd talk to your husband about how hard it is for girls in school if they are overweight, and remind him that the eating habits being established now, will follow through, and once they hit puberty, odds are good they will result in weight gain. Tell him he can eat what he wants, but ask for his help in raising your daughters to eat well. That means having his own area the kids don't see, to hide his treats. I did that on my own, perhaps he can do it with a little prompting.
Second - I lost 16 kg in two months ( 10 in the first ). I ate a lot of sugar, before. For all that, I am sure that cutting out soft drinks accounted for at least a third of my sugar intake. Give the kids milk or water at home, and ask that they only be given those things in day care, if you can. If they never get used to drinking soft drink, you're a long way towards cutting out sugar for them.
Third - have treats in the house that are sugar free, or at acceptable levels. If you keep their intake low enough, and also not every day, then their bodies will handle it better. So, try things like nuts for snacks. If you don't give them sugar based options, the dextrose ones will go down just fine, but they should still be a treat, ideally. It's just a whole lot better than sugar, if those are your only choices. You can buy puff pastry sheets at the supermarket, made with butter ( so, no vegetable oils ), and they have no sugar in them. When I REALLY want a treat, I buy those, and make fruit turnovers ( so, some fructose ). Then I put cream on them. Using cream instead of ice cream as a topping for desserts, is another easy way to cut out sugar. You can also get an ice cream maker and make your own sugar free ice creams. This is a great idea, because it means they can help to make it and to choose the flavours. If you use cocoa and dextrose, chocolate ice cream is possible, sugar free. There's tons of essences you can buy to make mint, or orange, or whatever, ice cream.
If they need a mid afternoon snack, I'd try things like a buttered crumpet, with cheese if they want. OR just a bit of cheese. Or an apple, the fructose comes with fibre so their body can process it better. Then, I would aim for dessert being only a few times a week ( because that's another good dietary principle for them to learn ), and aim for sugar free stuff from the recipes, for dessert you can move past cakes and make the cheesecake, or a mousse, those recipes are actually really nice, my family has not complained at getting one of those a week since I went sugar free.
And tell your husband, his metabolism will catch up with him, I used to be just like him, and ended up 16 kg overweight, it just snuck up on me. :-)
I hope that helps. You'll never get your kids sugar free, not unless you lock them in the house. But you can make your house an oasis, and teach them good principles. My son cannot eat chocolate, he goes hyper if he does. He soon learned and we'd often hear about a chocolate cake being brought in, and Calvin announcing he could not have any. So, it's possible to teach kids to avoid certain foods, although sugar is probably tougher, you can at least try to teach them to try to avoid it, even if they have it sometimes.