I would think that a crate would be the safest for everyone. I take my three(all together) on errands without issue. They stay put and don't make a peep, if they did I couldn't take them all with because there is no way I could fit 3 crates.
Has yours always been like this in a car? Or is it just recent? I know that when I got each one of mine, I took them individually with me everywhere. We went to drive thrus, gas stations, and places like that. They got used to people walking by and walking up to the car or reaching toward the window fairly quickly. My youngest did have car sickness and that went away--thank God.
I'm not sure correcting an anxious/stressed dog is the best thing. He probably needs to be conditioned. So maybe start with really high value treats, open door, get him in there and in a sit, treat, repeat until he understands sitting calmly means treats. Then maybe after several days actually shut the door and go through the same process, then move to starting the car, etc. It might take a couple months, but I think that it is going to require baby steps. It probably should be done even if a crate will be used.
Misty- Samoyed Mix, Tannor- Golden Retriever CGC
Robyn- GSD CGC, TC, Midnite-GSD CGC,TC, Brennan-Golden Retriever CGC, Batman-Husky/Greyhound , Apollo-GSD