Ilan, What I have done in the past with my bottomless pit Golden Retriever pups is a combination of management and training. For management, as you know, the best is constant supervision, but that can be tough will little children. The other management aspect (which is also difficult but critical) is to make sure that food is NEVER left where she can get it. Getting food off the counter is incredibly highly reinforcing and it will be almost impossible to break the habit if she learns that it is a great way to get a tasty treat.
For training, I heavily reinforce “4 on the floor” whenever the dog is in the kitchen. It doesn’t matter whether I am training or just working in the kitchen. If the dog comes into the kitchen (or wherever there are tempting counters) and has all 4 feet on the floor, I praise and reward. I also use these areas a lot for training Sit and Down. Once the dog starts to understand these commands, I’ll keep her on a loose leash and let her sniff or move around the kitchen. As soon as the nose goes up to sniff the counter, I’ll say “No!” (firm, not angry), “Sit” (or “Down”, whichever is her best command, or you can vary it). If she doesn’t respond, then I can correct for the sit or down with a leash pop and repeat the command. If she does comply, praise and treat. You want to catch her BEFORE she actually goes up on the counter, but when the thought is just starting to cross her mind. If you aren’t quick enough, give a sharp “No!” and leash pop to get her attention on you and give her a command. Then also give yourself a wrist slap for missing on your timing! 🙂 You can also use a “Leave It” command, but I prefer this to be an automatic behavior rather than a cued one – I never want the dog (especially one the size of a Great Dane!) to put a nose up to the counter sniffing.
Also, until this habit is broken, don’t put treats on the counter and treat her from there when you are training. Use a treat pouch or something. You don’t want her to associate that the treats come from the counter.
Good luck!