He says that he just wants to go home and get back to normal.
Take it from a real alcoholic/addict, he's going to get drunk. Sobriety is hard and recovery is harder. It's scary and tiring and overwhelming and nobody can do it for you. It's taken the greatest love of your life, alcohol, and walking away from it. Do you know how hard it is too walk away from him? Walking away from alcohol is 100 times harder. It can be done but it takes everything you have to do it. If your BF wants to come home, he's not ready. He still thinks he can manage it, which is not unusual. You would think he would be ready considering what he's been through, but he's not. He's going to come home, try to white knuckle it for awhile, and then have "just one" and it's going to be on again.
I suggest you wait on the "building trust" part because you still have a lot of lies and manipulations to get through. I would read the boards, try to get to as many Al Anon meetings as you can, and slow your relationship way, way down. This disease is no joke and it'll destroy you if you let it.