If the kids are older, can you start talking to them about what they are eating. And making suggestions, as PP said. Baby steps to preparing your own chips, or crumbing your own chicken to make nuggets ? Slowly one meal at a time, and see how they react ? Or what my mum used to do, was that each of us picked a meal we wanted to have during the week, that way, at least once in the week, we got a meal that you enjoyed particularly. Perhaps you can ask them what they would like as a meal, and try and suggest the healthier option ? Saying that how bout we cook it like this, and give it a try. Maybe trial it for a month ?
Or say re: Nutrigrain - say they can have it, maybe twice a week, and the other days they need to find another option (compromising). So slowly you remove it from the shopping list, but you are not cutting it out altogether. Perhaps also remind them that the healthier options will make them feel fuller for longer, so you can use that as information perhaps ? That they are growing bodies, and you need to look after themselves, and live a healthier lifestyle. Will make them feel better too, and better on your wallet too.
PS. do you do most of the cooking, or does your partner ?