Why is he picking up the dogs? I ask that b/c it seems like you have very regular contact w/him. That does not give you a chance to be away from it enough in my opinion. I share two kids with my X, and we literally speak once a week if that, and very brief, about the kids only. No nicey nice, just say what you have to say and move on.
That space has allowed me to go through the grieving process. About the engagement ring. No. Sell it, have it made into something else. Whatever. It's your's, not his.