Call the police and report possible abuse when it's happening.
Find the e-mail address for the local social services and give them a well written, non-emotional, detail oriented message.
Just say "I can hear him yelling nonstop and the kids are terrified"...shit like that. Don't give them anything other than imminent/immediate danger sounding shit.
If the dude has a wife, or a girl, that lives with him (you know, the one who pooped out the kids), leave her a printed out note in her mail box or on her car or something and anonymously tell her about the abuse (it is abuse). Only do that if you know you can get away with it while not being identified as the writer.
Complain to the landlord after you've called the police for two yelling events. "he doesn't stop yelling, people call the cops, I need quiet..."
Unfortunately there may be nothing you can do. But it just makes me wonder why a person like that would even want to have children to begin with? It's like people who have dogs and keep yelling at them to stop barking...they're fucking dogs they bark!! haha..
He's not doing anything illegal it sounds like...you could call child services but I don't even really know if that would be considered abuse...
you could just slip an anonymous note under his door late at night or something when he would never know, just expressing in it everything you are feeling and hope he gets the point, though I highly doubt he even thinks he's doing anything wrong.
He's disturbing the peace, you could call the cops...
I would try the nice approach first though. Leave a polite letter letting him know that you can hear their family altercations through the walls, that the noise is very stressful/distracting/annoying to you, and that you're hoping to settle this in a neighborly manner. Yeah, he's a psycho and he's being a bad parent. That happens when people are stressed out sometimes. Give him the benefit of the doubt, he might not know that you can hear him.
If that doesn't work aim all of your speakers the the wall or floor he's closest too and blast that shit! I used to have a neighbor who would play music all night long and presumably sleep during the day. I was FOREVER going to the landlord and complaining. I contemplated calling the cops, but didn't. Instead, one night I sat there and waited. Then a little while after the music went off, presumably the bastard was finally sleeping, I blared the heaviest metal I could find in my collection with my EXTREMELY loud stereo all facing downward into his apartment. My other neighbors probably thought I was insane because it really was so loud that the sound was quite off and it was mostly just screaming... You know what though? He kept his music a lot more quiet after that.
I'd say call the police and tell them that you're hearing lots and lots of yelling from that apartment, and you're not sure what is going on really and that you know that there are kids there. That should stir something up for sure.