I hate to say it, but sometimes death is the kindest solution to a pet. If an animal is in pain, it's really better for them not to suffer.
I grew up with pets, so I have two stories about how euthanizing an animals is a kind solution.
When I was 5, we had a dog who had lots of health problems. She couldn't walk up the steps well and was in constant pain from who knows what. Putting her down was so difficult but I still think it was the right thing. Her last moments on earth were still very good and if there is a heaven and all animals go there, I like to think she remembers those happily and doesn't remember too much of the suffering.
When I left for college, we had two dogs. They were like 13 and 11 years old. They had some health problems (one had seizures, one was nutty as hell) but were fine overall, and I loved them dearly. When my father moved in with his girlfriend, she didn't want the dogs so he dropped them off at a shelter. I found this out while I was in college. I wanted him to remove them from the shelter and put them down, because I couldn't imagine anyone adopting two huge dogs who are that old and have their health problems; people generally want a younger dog. It still breaks my heart to think that my dogs' last memories on earth were probably at a shelter, traumatized by the upheaval; he was pretty much neglecting them before moving in with his girlfriend, anyway, so that really hurts. I still haven't forgiven my father for doing that to my dogs (and still cry about it, am crying about it now), and the dogs must be dead from old age by now. In your instance, your actions would be more understandable, but at the same time, if the quality of life goes down to the point there's more suffering than not, I think putting your pet down is the best thing. It's going to hurt like hell and still make you feel sad, but you eventually realize it was the right thing to do. The last memories aren't going to be as bad as seeing your pet basically suffer and die off.
I hate being morbid, but I don't think I'd want to find my pet dead in my house, either. I don't know how sick your dog is, but if the health problems are bad enough, it could happen. I personally would rather make sure my current pet, a cat, had one last great day on earth if only for myself.