I'm a little concerned, too, about the fact that you think it might be possible to move in with him in August. Right now, he's drinking and you're accommodating/rescuing. Frankly, I'd be shocked if this DUI is his bottom.
Let's assume for the moment that the stars align and he stays sober for the next nine months. Is he a good bet to move in with? Especially with your young children? Given the history of lies and broken promises?
I'm not suggesting you have to break up with him or give up on any hope of his recovery. I'm just suggesting that at this moment, the future does not look promising for imminent permanent recovery and you risk a lot if things go bad and you are living with him.
If I were you, I'd consider taking any firm (or even semi-firm) plans to move in together off the table for the time being. It puts unreasonable pressure on both of you--it increases the likelihood he will lie about his sobriety and it increases the likelihood that you will turn a blind eye to the red flags.
If you're OK with limbo, then continue in limbo. Just be careful about forcing the issue--which is what tentative plans to move in together in August seems to amount to.
I'd watch it with the rescuing, though--even when it doesn't cause extreme disruption to your plans, things like fetching his keys after he's gotten himself locked up for DUI isn't allowing him to experience the consequences of HIS OWN actions.