I'm sorry -- that must be a hard thing to see for you, especially after such a long period of sobriety. I don't have any first-hand experience of this particular situation. It's heartbreaking evidence that alcoholism is never cured, just hibernating.
The "one more week" may be simple manipulation. I'm sure you're right that he's lying more to himself than to you. On the other hand, your T might have a point. I've heard that before. I have a friend who lost her father that way. He drank himself to death the night before he was going to inpatient rehab.
I don't have any advice for you. If I try putting myself in your situation, I think I would feel OK with giving him another week if he had a plan. If he said, "I'm gonna drink for another week, and next Wednesday, I'm going to start going to 90 AA meetings in 90 days," I might feel better about it. Have you asked him if he has a plan for how to get back on the path of recovery?