I have again given up on the dating sites (i'm still on it and I get a couple of 'hi's' each day) but I can't be bothered to be honest. I seriously fear that I will never really be interested again.
Re the dog. You're reading too much into it. He wants a dog. Let him have a dog. It might help heal his abandonment issues, it might not. It might make him feel less alone, it might not. He might be (unconsciously) trying to replace his family or he could just want some company in the evening and someone who is happy to great him when he gets home.
What's the situation with your second home? Was it a rental that he has decided to live in or is it a second home that you would use for holidays. Sorry if a bit intrusive, just trying to understand ...