Hi Trying, well actually that sounds like a solid idea - married but separated. You may want to consider a legal separation, if that is allowed where you live, just in case he does decide to drink and drive some time. You don't want to be liable for his actions.
Aside from that, if you can co-exist in the same house together and you think it's ok for your kids, well then why not.
Here is the catch though, do you believe that he is good for them or setting any kind of good example for them? I mean he is there, but he isn't really "there". But that's your call of course. As a bit of an aside, if you decided to actually separate, you could stipulate that he use a breathalyzer like soberlink.
I wouldn't leave the kids with him ever, you're right about that.. My Mom was married to my alcoholic Father until we were teens, she never had him take care of us or drive us anywhere.