Your DH invited him, he can't rescind the invitation, not if he wants to continue the friendship.
I think when your DH talks to Doug again about the details of the trip, he needs to explain that they are two adults that are traveling to the same place, that is all. Neither is responsible for the other. They can do things together, but are not required too, nor should there be any expectation of it. This way, Doug's issues won't impact your DH. Doug can do what he needs to, as well.
I presume that Doug is aware of his issues, and how his issues effect others. It would be good to have a discussion about the issues Doug has, how he can make sure they don't impact your DH, and , how and what Doug will do to help himself. If he needs your DH to say "Dude, you look anxious, maybe you should take your pill now" or something like that, fine, but, he shouldn't need your DH for more than that. If he does, your DH can say " I am not comfortable with that" and let Doug decide if he still wants to travel.