my cat has diabetes. He gets 2 shots a day (5 units of vetsulinx2) and we give him a special diabetic canned food at night. He tolerates it really well from me. If anyone else gives him the shot, he takes off and we can't find him for an hour.
A friend of mine has a diabetic dog and says giving him the shots is easier than giving them to my cat since he has so much more scruff. He does require more insulin though so she goes through a bottle of insulin more often than I do w/ my cat. Obviously.
Don't have insurance for the cats but it is my understanding that if your dog was previously covered and this is not a pre-existing thing (like human insurance) that they'll cover visits but probably not medication. I could be wrong.
Good luck. Our cat has had diabetes for about 4 years now and he's going strong, his weight fluctuates but overall, he's a badass. We think the steroids in the insulin make him think he's the bully since he kicks a lot of feral cat ass nowadays.