You mean you used weasel words? You gave yourself an out by saying "probably?"
Does she deserve a beating, you mean? You answer me yes or no. That's it. No weasel words.
For all three of those offenses, she deserves to be punished.
In abstracto, any number of punishments are conceivable, all of which are just, which can be carried out by any number of different agents.
I would like to remind you that, in the OT, the Law of Moses prescribed stoning for an adulteress. Unless you dare blaspheme and accuse God of injustice, then you must admit that it is potentially just for an entire community to stone an adulteress to death.
In concreto, that is, in this or that existentially realized circumstance, it may not be the case that it is just to stone an adulteress, because various circumstances prevent it.
#1 and #3, There are all the laws on the books we need for legal recourse, no beating required.
That's why I withheld judgment. If the State reserves the authority to punish, then it's probably unjust for a husband to beat his wife in those circumstances (though, what other man would hold him accountable in a court of law if he did; the sheer anger/passion which would be invoked in such circumstances potentially could constitute a very significant mitigating set of circumstances to his guilt), since he doesn't have the authority to do so.
But suppose that there are circumstances in which the State dispenses the authority to punish in such circumstances to the paterfamilias. Then yes, I think it would be perfectly just for a man to beat his wife in such circumstances. She deserves punishment. Beating is a proportionate punishment (at least, if it is not too little, it is at least not too grave a punishment), and the paterfamilias would have the authority to carry it out. Therefore, it would be right for him to beat her.
#2, what punishment do you have in mind for adultery that would include corporal punishment?
The Law of Moses prescribed stoning. Given the fact that a God whose very name is Justice Itself prescribed this penalty, you can't argue that this is, in principle, out of the question. If the State permits a husband to beat his wife in such circumstances, then by all means, the husband, it seems to me, would have a right to do so.