Originally Answered: Would you leave him?
Kids don't ask to be born, they don't ask to be here, so him yelling at his kids and wanting them to be quiet all day is a form of abuse. Kids like to explore, they can be inquisitive, they need adults to spend time with them, help them with homework, play outside with them, etc.
Your husband shouldn't be taking out his personal problems on the children or you, if he wants to vent to you, that's ok, but the kids don't need to be hearing that at all.
I wouldn't leave him, I'd think he is stressed with work and that he needs to change jobs or work less hours, and I'd have a talk with him about how he is coming across to the kids, for children, the home should be a sanctuary, not hell so explain that to him. He started this behavior after the third child was born, so maybe the stress of having three kids is getting to him, but he should have thought about only have one kid or none if he didn't want that responsibility.....Anywho, this would be the one time I would say that maybe counseling for him or marriage counseling for the both of you might help. Or even him having friends to hang out with or take up boxing classes or hitting the gym, might be a good way to relieve some stress and be happier. Another thing, how's the sex life ? Are you still actively showing him that you love and appreciate him ? That you are there for him ? That might have a positive affect on his overall mood.
Work on this marriage before throwing in the towel, he is not cheating on you, he wasn't always behaving the way he is now, find the cause of the change and see if you can work on it. Maintaining a good sexual and emotional connection with him will help :) but if he continues with the anger issues with you and worse yet, the kids, and he doesn't want counseling, then that's not a good environment for the kids to be exposed to, or you.
Best of luck