I would choose a grain-free diet that uses turkey, fish, or beef as the protein source. Do not feed a protein that your dog would be allergic to. Chicken, venison, and lamb are considered to be warming according to Chinese food therapy so I would avoid these especially in the summer. If you do switch the foods, do so gradually phasing into the new diet over a week or two. Initially feed according to directions and later you can cut back slightly in order to reduce calories and you can add in some cooked green beans to add more volume.
Have you tried ARTHRO-IONX? It might make your dog more comfortable so you can walk her a little. Begin exercise gradually so she does not become sore. OMEGA 3,6,9 also helps to decrease inflammation and can reduce joint soreness. I would also give PROBIOTICS to improve the intestinal flora; The bad bugs can cause weight gain.
I would also consult with a veterinary chiropractor. Proper alignment allows for better movement.
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