However if I ask him to leave I have no idea where he would go.
Here is my experience.
I have asked/requested/forced my husband to leave our home when he relapsed. Each time he has left wherever he goes from there is not my problem and eveytime he always finds a hotel, apartment or sober living environment. There are lots of options for housing or temporary accommodations in a variety of price options. He just needs to go look to find something.
My husband (and yours!) is a grown man. IF I had to leave my home because I was doing something that was effecting our children in an unhealthy way then I would definitely be able to find somewhere to stay. Regardless if I was drunk out of my mind I would be able to work my phone enough to call a friend at the very least or book a hotel. It's really easy peasy.
You worry about you and your kids. Let your husband worry about himself. That's part of him taking responsibility for himself and he can't do that if you're taking responsibility for him. It's not really a consequence (this is not to be confused with punishment, you're not punishing him you're creating a better living environment for yourself and your children) if you tell him he has to leave and set up a hotel reservation for him. He needs to worry about that and do the footwork himself. And if he doesn't then that's his own choice.