It sounds like your dog may need to be wormed. This may be two different problems. The coat problem could very easly be cause by worms and this can be an easy fic with the purchase of a product called Tasty Paste. Small yellow tube with the weight line on the plunger so it is easy to set easy to give,by mouth. You also can give some Vit. E oil , or a little bacon grease in food two times a week. Just a teaspoon. The product I perfer for Fleas, ticks and  mosquito's( which helps to prevent heart worms) You would not be able to start until the other had been out of the system a month or you could overdose the dog. If you do you will know it the dog will throw-up and be drooling. Wash dog in lukwarm water severl times if this happens with dawn dish soap. If it does not help in an hour take to vet.You might just want to take to vet to have the vet worm the dog this firt time anyway to get all worms and then the medication must be given again two weeks later to kill all eggs that will rehatch. T. Canaday Emergency Livestock Manager Spencer OK