Alcoholism and cheating don't go hand in hand, he's trying to get away with one thing by blaming the other. Sure drinking too much is not going to help but most people manage to get drunk and not cheat.
He may be having some kind of mid life crisis, if this really is new behaviour and a lot of the time it doesn't end well, it's not just that he's fallen for someone and couldn't help it, he's actively looking to cheat on you, so in this circumstance I'd say yes he's very likely to cheat on you again.
Even if you don't plan to divorce, (which you should) you need to seriously give him a wake up call by getting him to leave ASAP. Be very firm and tell him you are separating indefinitely until you can make a decision and hopefully by then it will be the right one, and that it's over.
Op, what you had with him is lost forever, you'll never have that warm cosy trusting feeling again, the you and him against everything feeling, he's the enemy now, for the very long foreseeable future.
Put yourself and Dc first, protect yourself, he has ruined your family unit, him alone. You have no guilt saying no.