First, there would would be a mod note. Then, there would be a warning. After a few warnings, the undesirable individual would be banned from the village. If they tried to sneak back in, wearing a trench coat and a false mustache, they would be banned again, more forcefully. For things like disagreements that escalated to violence, every village had a pit. The combatants would be thrown in there and left to sort out their differences.
Actually, though, for stuff like this:
They were presumably dealt with in the same way that we deal with these things today. It’s not like we involve the police for that. These things are handled privately, or in the local community. They might have been handled a bit more hands-on. My impression is that the bar for resorting to violence was a bit lower in ancient times, in most places.
For the husband beating his wife: Yes, he would presumably keep at it being the house tyrant.
For the guy going around beating people up, and also robbers, thieves and stuff: More interesting.
Anyway, villages aren’t really my area. But let’s have a look at the city of Rome, which had about a million people in 100 AD, and was in many ways much like any large modern urban area. (Seriously, why are we talking about hovels? The ancient world was urban and sophisticated. That is, if you didn’t live in the boonies, like… I dunno, Germany. But who wants to live there? Unless you’re German, I mean.) A lot of the time, the answer will be: Vigilante justice. One of the most amazing things to me about the Romans is all the things they were able to do without. The city of Rome went for the longest time without a police force. (One unfortunate consequence of this was that at times, mobs or gangs were able to more or less take over the city. They could be handy as a political tool.)
By 100 AD, though, it had acquired a police force. Actually, two: The vigiles and the urban cohorts. The vigiles were the night watch and fire department, and would also deal with disturbances of the peace, petty crimes, and things like chasing down escaped slaves that couldn’t run fast enough. The urban cohorts would do more heavy-duty stuff like riot control.
Even so, good luck finding someone to investigate your robbery or even your homicide. If you could find the perp, though, and also find someone to hold him down, you could drag him into court yourself. If you had wealth to protect, you would probably want to spend some of it on bodyguards. Also, you probably wouldn’t go outside after dark if you had any sense. No street lighting.
Punishments: No prison system. Death, floggings, fines, restoration of nicked stuff. Also, quite a bit of exile. Hope you have some friends in the next couple of provinces over. I also hope you won’t miss your property, because we confiscated all of it. Good luck.