I am married to an alcoholic for 18 years. Like your alcoholic mine told me his stories and how he managed to not drink. Oh he was managing alright, he was not drinking - sure but he was using pills that I was not aware of until AFTER we were married.
He slowly slipped into depression while I was pregnant with our first child and 6 months after she was born he drank again.
I echo what Lexiecat already said, your AB did not "relapse" he is just progressing in his disease, like they all do.
If all the "help" and "love" I put in over 18 years couldn't help my alcoholic then an early long distance relationship won't "help" your alcoholic.
Don't mean to sound harsh by any means, just being truthful.