At my synagogue, kiddush is set up in the back of the room while Shabbat morning services are still going on. Most of the members are middle-aged or older, though there are a few families with young kids, and in general everyone gets along. However, there are a few kids (who are old enough to know better!) who always take food from the kiddush table during services. Not only that, but they stick their hands in everything so that by the time services are over, no one really wants to eat the food anyway. Is there anything to say to their parents to help the situation, or anything else we can do?
Taking the "Kid" out of "Kiddush"
When I was a kid, part of my "job" at services was to help set up kiddush. I poured all the little cups of grape juice, and even a couple of shots of Scotch for some of the old men. Along the way, if I happened to sneak a cookie or two, no one minded at all. The whole process kept me occupied when I otherwise would have been antsy in services, and it actually got a necessary task done. Even in my current community at Minyan Tikvah, I think it's well-known that a benefit of helping to set up kiddush is getting a sample.
I wonder if you or someone else could engage these kids in helping. By the end of services, they're probably hungry and a little bored. It seems totally natural to me that a big table full of food would be impossible to resist. Whoever currently sets up kiddush could invite them to have a particular job, say, putting chips in a bowl or washing fruit or something else developmentally appropriate (i.e. not pouring Scotch). The kiddush coordinator could establish that one of the requirements of helping is washing hands first. That way, the ick factor for the whole congregation could be drastically reduced, too. The kids would be occupied, their hands would be clean and they'd be able to snack in a way that fit into the overall structure.
Since you ask about involving the parents, it may be worth having the adult in charge of kiddush approach the parents to say, "We'd really like to give your kids a task. Do you think they'd like that?" Hopefully the parents will go along, and you'll be all set for neatly arranged, germ-free cookies.
If, for some reason, you don't want the kids to help, consider putting aside pre-kiddush snacks for them so that they're not contaminating everyone else's food. Truthfully, the idea of parents taking kids to Shabbat services without a cart-load of snacks is kind of hard for me to believe. Maybe there's a polite way to tell them, "Your kids seem like they're hungry. Would it be all right if I brought pretzels for them next Shabbat?" You're offering to help, which is nice, and unless these parents are really clueless, hopefully they'll see that they ought to be feeding their kids.
With my 2-year-old, we've found that lollypops really work wonders at services. One lollypop will typically last her for two hours and occupy her hands, her mouth and her attention. Yes, it's sticky and perhaps not the most sanitary experience, but I do think it's preferable to toddler hands in a bowl of kiddush goodies. Plus, it's something that makes Shabbat special for her.
A bag of Dum Dums will cost you pennies compared to the aggravation it sounds like this situation is causing you and other congregants. Again, it's a good idea to ask the parents first, but hopefully they'll either be open to the idea or find ways to keep their kids occupied themselves.