Your dog may have a problem in collagen metabolism, or production such as:
cutaneous asthenia (dermatosparaxis, Ehlers-Danlos syndrome) which are syndromes characterized by defects in collagen production. These syndromes can affect the skin integrity (stretchability) and can cause joint laxity, and other connective tissue abnormalities. Diagnosing these abnormalities is possible through skin and collagen biopsies. The skin usually shows more than just hair loss though. So your dogs two problems may be unrelated.
There may be no cure for these problems, but, vitamin C, may indeed help. Dog's do make their own vitamin C, but your dog may have a problem with vitamin C production, or just not make enough. Vitamin C may be very helpful for your dog.
Other medications that may help your dog as follows:
1. Polysulfated Glycosaminoglycan (PSGAG):
PSGAG is approved for use in dogs for degenerative or traumatic arthritis. PSGAG increases the synthesis of hyaluronic acid, proteoglycan, and collagen in joints.
2. Pentosan Polysulfate Sodium (PPS):
PPS helps damaged joints. In canine models of osteoarthritis, IM administration of PPS significantly decreased overall cartilage damage.
Orgotein is a water-soluble metalloprotein containing copper and zinc. It scavenges free oxygen radicals which are involved in the damage of joints in dogs (and other species).
I would also add an antioxidant combination supplement for your dog that includes: vitamin E, selenium, vitamin C (of course), beta carotene, zinc, alpha lipoic acid, and coenzyme Q10. Use 1/2 of a human adult dose and frequency of administration. All the antioxidants work together, add extra Vitamin C (500 to 1000mg) twice per day.
You may also benefit from a holistic vet. Please google: American holistic veterinary medical association, and the Chi veterinary institute, and vet-stem websites.