Hi Bailey! and Dad!
Sounds like the first few car rides Bailey did not have the best of times, the vomiting and then vet! nobody's fault, Bailey just has had a few bad experiences with the car..the car sickness, i have googled it and it seems alot of it it stress (like first bringing a pup home), but maybe some others can chime in on wether their dog's have true car sickness, and what to do.
I think what you are trying is good, associating the car with good things..try some treats too! Also, are you taking Mr. Bailey out for fun trips? If you can get him in the car, take him fun fun places, I know he is young, so maybe friends houses, parks where you can romp with him, ect. Just as long as it is positive. Start slow, like him in the car with a treat, then maybe turn the car on, then go for a spin around the block. Take it as slow as Bailey needs. I dont know if you have tried it but put his crate in the car so he feels more comfortable in his den, not to mention it is safer.
Also, make sure he has went to the bathroom, and ate his lunch/dinner earlier, so less likelihood of an upset tummy.
hope that helps, and I am sure you will get other great advice, good luck
there is also a lot of links out there if you search google for car sickness, dogs in the car, ect