This is really a hard one and, in my head, I know what the *right* thing to do is, but not sure if I could do it. I'd have to see how I felt about my relationship with the parents.
OP, you've stated these boys have all been long-term friends and there's been several vacations where all of them went. Now the one boy is not pleasant to be around. Unfortunately, they are all still friends and it's going to be quite obvious the boy when he's left out. And there will be no explanation. It's just like you guys are kind of "ghosting" him for lack of a better term. I don't like that and I always feel honesty is best in the situations. Just imagine how hurtful being left out will feel to this boy (and maybe how his mother might feel). We've all read numerous "left out" threads here on the DIS and moms are usually in a lot of hurt over why their child is left out.
SInce you are taking all the other boys, the right thing to do is let the parent(s) of this boy know why. If you weren't taking any of the other boys I would agree that you would owe NO ONE an explanation. This is a little different. He is being excluded (and for his own fault) but the boy and his mother/father may not be very self aware. At least you have "the dead dog" incident to use as an example when/if you discuss with the parents.