
I've had my adult rescue dog snap at my toddler over food (toddler walk past dog while dog was eating from his food bowl - dog turned and snapped)- it happened the once and didn't get chance to happen again as we got on top of the food guarding issue ASAP.
A couple of things that helped - dog is to be moved away from children when they are eating - the dog needs to respect the childs right to eat in peace and it also removes the opportunity of the dog stealing food etc.
The dog gets no attention from children while they're eating, the dog doesn't get touched/spoken to/looked at (I know this sounds like a Cesar Millan thing, but this worked, long before we saw Cesar on TV!!)
Dog doesn't get to pick crumbs/food off floor that children have dropped.
The dog never gets fed tidbits and does not get to eat leftovers, even from his own food bowl. If they are used to eating left-overs they get excited with anticipation - this can be removed by them learning they don't get food other than thier own (this may not be general, but worked with my dog).
Kids get to put dogs food bowl down.
Most important, the dog needs to know that you will not put up with it, it's hard to explain but if you believe it, the dog picks up on it (I know I sound like a loony, but they do know when they are faced with a push-over or not).
9 years after that first snap, the dog has never done it again, & I'd trust him with my kids as much as you can trust any dog, and he has no problem with anybody going near his foodbowl.