This may sound funny, but I think you may be able to solve your problem by feeding your dog more vegetables, and switching to
raw food if you can. I've fed my dogs raw food for 10 years now, and I noticed that a lot of behavioral issues went away. I have one dog who is extremely food motivated, and a tremendous hunter, too - the sort of dog who you would think would get into everything, because she is so driven. She's a black lab/ St. Bernard mix who digs like a badger, and has killed a
deer, otter, countless small animals, and once pinned a bobcat in our creek. That was a memorable late night
experience when my husband pulled her off the bobcat, not knowing it was a bobcat...
Anyway - she's been a handful. And she used to break into our fenced garden, both to eat veggies and fruit and dig up
voles. Massive destruction. She also ate an entire bed of garlic - twice! I switched to leaving the
compost heap outside the garden, and that seemed to do it. She started supplementing her own diet (which was already raw meat and raw and some cooked veggies), and left the garden alone.
My husband and I see a nutritionist, Dr. Steve Nelson, a really knowledgeable guy. He also helps animals. He says that animals "eat what they need, not what they want" - which means that if they eat something weird, they are innately trying to solve a nutritional problem.
Here are his guidelines for feeding dogs and cats, my comments in (parentheses):
1. Home cooked or raw food is best. About 80% protein, 20% vegetables and fats, no fruit. (The ratios are slightly different for cats vs dogs, it's best to look these up.)
2. Most dog and cat food sold in stores is not good for your animal.
3. Dogs and cats are carnivores.
4. Protein from
beef, turkey, chicken or lamb - free range or organic is best. One organic raw egg a week is good. (He's hesitant to recommend fish, as he's found its very high in parasites. If you use fish, it should be cooked, not raw.)
5. Grains should not be a part of your dog or cat's diet.
6. Animals eat what they need, not what they want:
- If the eat their stool, they are lacking digestive enzymes or having digestive problems
- It they eat socks, they want fiber
- If they eat grass they have a sour stomach
- It they eat women's panties they may be low in iron or other minerals
7. Dogs and cats are hyperchlorhydric by nature. (So, they digest through having highly acidic stomachs designed to eat protein and digest bone, not sugars, carbs or high amounts of fat.)
8. Please do not sleep with your pets. (He sees a lot of people and pets with the same parasite issues...)
So, those are his recommendations. I've fed my dogs raw food for about 10 years now, there are specific guidelines for what vegetables are safe for most dogs that you'd want to look at if you consider this option. The short list - they shouldn't eat onions, brassica veggies should be cooked, parsley can irritate their kidneys, and legumes are hard for them to digest.