22% fat is clearly not the problem. Take my dog for example, she has been on 28% fat for about 7 years now. I think your problem lies in what I hightlight in bold below:
INGREDIENTS: Rabbit Meal, Salmon Meal, Tapioca, Chicken Fat (naturally preserved with Mixed Tocopherols and Citric Acid), Tomato Pomace, Pumpkinseeds, Sun-Cured Alfalfa Meal, Montmorillonite Clay, Natural Flavor, Sea Salt, Vitamins (Choline Chloride, Vitamin E Supplement, Ascorbic Acid, Niacin Supplement, Biotin, D-Calcium Pantothenate, Vitamin A Acetate, Riboflavin Supplement, Thiamine Mononitrate, Pyridoxine Hydrochloride, Vitamin D3 Supplement, Iodine Supplement, Vitamin B12 Supplement, Carotene, Folic Acid), Peas, Brewers Yeast, Potassium Chloride, Minerals (Zinc Proteinate, Iron Proteinate, Manganese Proteinate, Copper Proteinate, Sodium Selenite), Dried Kelp, Cranberries, Blueberries, Inulin, Freeze Dried Rabbit, Freeze Dried Rabbit Liver, Dried Enterococcus Faecium Fermentation Product, Dried Lactobacillus Acidophilus Fermentation Product, Rosemary Extract, Freeze Dried Rabbit Lung, Freeze Dried Rabbit Hearts, Freeze Dried Ground Rabbit Bone.
I count about 10 things clearly non-species appropriate, unless you truly feel your dog is an omnivore, they should not be in the ration. I see a few other things I highlighted anyway because I'm not really sure why the heck it's in there. Rosemary Extract doesn't seem to be used as a preservative for any fats, so that gets a strike as well. This is food as advertised is 2% fiber. I myself find that very hard to believe. Those sources of fiber I have underlined, and probably more I don't see. Best guess about Montmorillonite Clay is it's in there to act like a fiber, not because there is any thing special about dirt being dog food.
IMO, your dogs problems center around your food choices. Unfortunately, the Vets food is probably no better supporting industries decision to feed dogs like omnivores.
I think you can solve your dogs problems by making better choices in nutrition. Feeding species appropriate is good start. Some will make it sounds as simple as tossing a piece of meat on the ground. Reality is dogs and cats are top of the food chain and their nutritional needs are complex, more so than that of humans. A species appropriate diet where you know you're getting everything your dogs needs no questions asked, people turn to Abady Granular Feeds. Don't be scared of 800 cals per cup. That DOES NOT mean your dog will get fat. All that means is your dog will need to eat less.
You can try the raw prey model if you want, many have great results with that, but then again some unfortunately end with a trip to the emergency vet because they didn't do there homework. You can't miss with Abady feeds, it's right every time and species appropriate and at 800 cals per cup can blow the doors off of any cup of raw.
Abady has a website, read about what they have to say about canine nutrition and the benefits of feeding dogs like carnivores.