Probably, but there's got to be more to it than that. I've been drunk. I've never shot my offspring while drunk. Ditto literally millions of other gun owners who drink.
As you said...has to be more involved. The family dynamic can be so complicated but letting things go this far shows deeper problems than what we are seeing.
There have been moments that I have been so mad at one of my sons it was good I did not have a gun in hand as I would have used it as a club....shooting him, never an option.