Times as trying as this make you think far deeper than you normally would about these things. The question you need to ask yourself is whether these little things really are as bad as you are thinking right now?
What I mean is that when a time like this comes, you think about what is really best for your family. Would life really be better without him? Or are you taking the stress out on him?
The fact that he told "anyone who would listen" tells me that he needed to talk to someone about this when sober. And because it was all bottled up (no, that wasn't a bad pun), when he was drunk, the thing that he had been keeping inside came out to anyone who would listen. I do this when drunk as well. I don't get drunk very often in order to avoid regrettable conversations, though.
I he really no support at all? If you feel he is not supportive enough in this terrible time, and this has resulted in you feeling like the relationship is dying, then the two of you need to talk more about this.
Or, maybe he is just a self centred twat. If you want to find out which, I suggest letting him tell you how he feels, then once he's got it out and is nice and placid, tell him gently how you feel. Try not to shout. Sounds like there's been enough shouting on both sides.
Also, I agree that the Chinese whispers that resulted in the telling of parents was the act of a twat.