Sounds as though the partner you are working for is the problem really. There is absolutely no chance at all this would have been initiated by HR and he could have done nothing about it, I promise. HR in law firms do as they are told by the partners, who obviously own the business. That's a little bit simplistic, but you understand where I'm coming from.
It sounds as though you might be right about him instigating it then feeling guilty. If he's a bit of a temperamental type of person, if you caught him in a dodgy mood he might well have gone yelling down to HR telling them to do something about it, then felt guilty later. Difficult to work for someone like that, as you know! Difficult for HR as well, not knowing whether they are coming or going!
If HR are supportive make the most of that, they won't have any 'power' as such to discipline you or not discipline you iyswim?
I'd be inclined to think about just letting it go this time. Be as honest as you can be with him when you need some support with regard to your home life, and maybe think about following up conversations with emails if you think that might help him with being a bit more consistent.
As you know, working for people like that, you do sometimes have to swallow your pride a bit and put up with things - it does come with the territory occasionally. Doesn't make it right of course. But if you are good at your job and can put up with the occasional madness, you might well reap the benefits, and at the very least, other people within the firm will know full well what you are putting up with!
The other thing to think about is what would happen realistically if you made a complaint... There are good and bad sides to most jobs. Good parts of working in a law firm are often financial, some others as well. Bad parts, especially working for a Partner, can be inconsistency, frustration and a feeling of powerlessness. But you need a dose of realism about what is and isn't possible to change, depending on the person you are working for. If you are able to put up with this person for a while, opportunities to work for other partners elsewhere might come up and if you've done well with this person, it could stand you in good stead and give you a good reputation elsewhere - as you've said, most don't last long with him!