So i was out in the wild exploring when i came upon a stray dog i had it follow me and lead it back to my house in solitude where i told it to wait after i went out and did a bunch of quests and got new followers i came back and the dog is still there i cant talk to it any more to get it to follow me though so i guess i got a pet now?
I discovered a stray dog as well, which I let follow me. We fought a number of battles together, then I figured I would give him a break. I left him at my house in Whiterun and when I returned hours later he was gone...
Your lucky your dog at least stuck around. Apparently I didn't feed mine well enough or something, so he split.
I have read about others having the same issues as you and I. Sorry but I have not discovered a working solution yet. Just know that your not alone with your companion issue(s).