Think I should have taken more care over that, Oblomov. Anger management is a bhavioural issue for people who can't control how they express their feelings (especially negative ones). When somebody loses it all over the place, causing them to have problems at work and so on, it's possible they have a problem which can be fixed with some training - anger management classes. There can be other causes of random rages, though, it's not always that cut-and-dried.
Domestic abuse comes from a belief that it's all right to rage, shout, sulk, complain and/or hit out at your own family - in other words, to treat your nearest & dearest worse than you would treat a shop assistant or a work colleague. So, when we ask if they also shout at other people, we're trying to see if they're generally horrible or only nasty to their own family, iyswim.
If they are only nasty to their own family, it's domestic abuse. That is cut-and-dried.
You were talking about shouting at kids - I don't know whether you mean the odd bit of yelling when everything's gone wrong, or shouting at the kids a lot because you're stressed out. If the latter, then I'm afraid you really should look at it closely. Sorry for being too blunt before.