I'd sit him down when he gets home from work tonight. Maybe, if you can, get family to care for DC, and say to him: Something very serious has happened. We need to talk. That will get his attention.
Then ask if he really wants to be one of the cliched statistic of marriages that collapse shortly after the second baby is born because temporarily the wife is distracted and has baby weight, and domestic life is temporarily tough.
Is he really that weak person who puts his willy before his children? Because you know he's checked out of the marriage and you are giving him one chance to check back in, because you believe he is better than that. You believe he is not so weak or selfish or stupid that he'd chuck away everything during the well-known most difficult year in all marriages - the year the second child is born.
If he starts blustering, just look him in the eye and say: I know what's going on. If he tries to question you, just repeat calmly, I know what's going on. Are you sure you want to put your aching balls before your newborn baby?
I might even hand him the baby and say: Look at this person. You made them. They are your responsibility and you have One Chance to step up, be a man and take proper responsibility. We love each other, we might have lost sight of that because I'm covered in baby puke and baby fat for now, but I thought you were man enough to see beyond that, to know that's a very short period of time. You can be strong or spineless. You can choose your penis or your children. But don't lie and muck about. We both know that is the choice. You choose tonight. Which has priority - the young children you brought into the world or the aching balls that want to sink into some woman at work who currently doesn't have baby fat and baby puke all over her, both of which are products of you bringing a child into the world.
Pre-empt him saying he's fallen in love, by telling him it's a cliche that men run off in the year the second child is born with the first woman who pays them attention. She seems so desirable in contrast with the domestic harridan looking after his children. But in reality it's just an escape route because any woman not covered in baby puke and looking sleep deprived is more attractive. But if he actually makes an effort to connect with his children, to love them and raise them and be a proper dad, and to love you and have fun and adventures along the way in his marriage to you, he will have a far happier more rewarding life than if he just focuses on scratching his current itch.
One chance: babies or balls. Choose tonight.
And don't give him a second chance.
I so despise men who think their willies are more valid than their children.
Sorry for this essay but I truly think too many men are allowed to scuttle off at this tough point in a marriage these days. We have become so morally spineless and I think whatever he chooses to do he should do it from a point of absolute clarity. If he does scuttle off it's because he loves his willy more than he loves his kids. He should acknowledge this. Don't make it easy by just silently gathering the children and coping with the pain. Make it as uncomfortably honest as you can.