I tend to think he wasn't quite as "functional" at home as he would like to believe (or to make you believe), if your son is saying he's leaving if he goes back to drinking. Have you talked to your son about why he said that? It might be a good conversation to have. And maybe your son should talk to his dad about how the drinking affected him.
I would turn down the offer of the breathalyzer. You do NOT want to be in the position of being the "booze police."
I'm a sober alcoholic, myself (six years sober) and I think he would benefit from AA for the fellowship and guidance of other alcoholics. Stuff like whether O'Doul's is a good idea, for instance, or the advisability of being around alcohol socially early on. You don't want to be his "sponsor" or be researching stuff for him, either.
I really hope he stays sober, and he might very well do that. For me, AA has enriched my life in countless ways, way beyond just keeping me sober.