Could you wean your family onto low carb treats? There are low carb brownies, cookies, almost everything. The big exception is salty/crunchy stuff like chips, but perhaps they'd take to nuts?

I grew up in a family where Mom was pretty tyrannical about the food we had in the house, so I'd probably follow in her footsteps if it were up to me. As we grew older we knew we could get our crap-food outside the house, but inside... nope. I think we knew from an early age that Mom was pretty iron-willed about such things and those battles weren't going to be won.