I think the dog's only close relationship was with the dad. Mom apparently wasn't aware of how big he was getting, and after having him for two years she apparently had enough. Dad seemed to like him - but didn't do any training. When we were introduced to him, he was wearing a prong collar instead of a regular collar, and dad relied it to counter the 120 lbs of dog. (My daughter is opposed to any aversive training - but even among trainers who use them, they aren't supposed to be constantly holding him back.)
As near as I can tell, they rarely took him in the car, so he didn't get used to it - but I suspect there's more that we'll never know. They got him in the car by crawling in first and crawling out the other side and closing the door on him. And then we went to meet him, loaded him into our car, and drove him 3.5 hours away from anyone he'd ever known. He was on his best behavior for a while - I expect he didn't want to make us mad. Once he got comfortable that we weren't going to send him away, he started showing his car anxiety even more.
But we're making progress. I'm spending 10-15 minutes a day helping him to be less afraid. I go sit in the car with treats and an open door and tug on his leash every once in a while to remind him I'm there with treats. Eventually he wanders over and takes them. I've got a sniffing game he loves (treats hiding underneath tennis balls in a muffin tin). I put it on the floor of the car and after he ate the treats today, he played his game and found all of the treats. He didn't get his body in the car - but his head and front shoulders were in the car.
Baby steps.