This is obviously a psychological issue.
Drugging him is not the answer.
If he is afraid of the sound, put music on in the car and if you can, pipe it to his area.
If he is afraid of the sight of the vehicles, get those baby shades so he can't see out the window he is sitting at.
While you're at it, get a doggy seatbelt to keep him in one corner.
Keep his favorite toy or blanket with him to keep him feeling "safe".
I strongly suggest trying to figure out how you can keep him at home instead of taking on these terrifying trips for him. He is obviously scared to death. Fearful dogs can act out in odd ways - ocd chewing, biting or nipping, agitation, etc.
Can you get a pet walker once a day? Maybe a teenager who can take him on a 10 minute walk for $5? Why do you have your parents watch him anyway? Do they enjoy it or did you plop it on their laps? Just wondering if you are leaving him over there just bc you haven't worked on a solution to keep from having to cart him everywhere. It can turn into a serious issue for the dog, and if it means you might have to spend less on something "extra" and do something that will help your dog, then you might have to make that sacrifice.
Quick story about fear and dogs. My friend's dog was petrified of thunder storms. After a bad summer, this dog had chewed his leg down to bone, destroyed furniture, went on anxiety and depression pills, and had a heart attack. There wasn't anything they could do to prevent storms (he hid in the bathtub during them), but you have a situation that might have an alternate solution.
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