I'd ask your sponsor to show you the term "Dry Drunk" in the Big BOok, this is a trick question becasue it isn't in there. Like Dee said, it is a disparaging term. A sponsors job is to bring a guy through the steps, has he done this? are you interested in doing the steps? If not, I'd drop him, it is perfectly fine to fire a sponsor, believe me, I've been fired multiple times.
Regarding the relationship, I think the Joker in Batman one said it best, "don't mess with another man's rhubarb".
(I know this is sexist language and personally don't refer to woman like this-blame it on the Joker) but I do believe he was on to something when he said it.