I think you had a great first ride. It sounds like you have a good horse. I'm remembering now how terrified I was in the early days when a car came up while I was riding my big guy on the road. Since I live on a busy state highway, one of the resolutions to that issue was to move winter feeding out to the end of our driveway. Twice a day the horses are standing out there for hours watching a continuous parade of tractor trailers, motorcycles, emergency vehicles, boats or snowmobiles on trailers covered with flapping tarps, and more. Now if they are lying down when sheriff's car goes by at 90 mph running lights and siren, they don't even get up. it's been a many years since my big guy reacted to car when I'm on the road. I realize that isn't practical for everyone. Anyway, he will be less excited after the trip becomes routine. Meanwhile, positive mental imaging can enable you to fool your horse into believing you aren't scared.
One other tip on the whole car thing -- what is the worst that could happen? What did you previous horse do to inspire such terror? The one thing that helps me remain calm and confident now is I know my big guy will respond to a one-rein stop RIGHT NOW. No matter what spooks him, (and he will always be a little spooky, you can't desensitize a horse to everything) I know I only have to stay on for 10-20' of excitement and he'll calm down. Even I can stay on for 20'.
As far as rushing home, I don't like the idea of trying to ride past the driveway. One of my first rules of horse safety is never start a fight with your horse that you aren't sure you can win. Here are two suggestions that will solve the problem without the drama. First, when you get back to the barn, instead of taking off the tack, do some work right by the barn. Some trotting in circles, backing, leg yields, etc. or if you've had your fill of excitement, lunge him for 5-10 minutes.
Second, when you've finished with all that, tie him to a tree and let him stand there for an hour or two. It's very good practice for him anyway, and it's the perfect time to do it. The idea is to take some of the attraction out of getting home.
Good luck. I think repetition will solve most of your concerns.
LOTS of great suggestions here.
a) we will soon be moving Harley to our house where he will be in a paddock adjacent to the road. Same road I ride on. Currently, is is in a field a the end of a long laneway so no exposure to traffic. I do think he's ok with cars as I've never sensed him flinch before, but I am nervous about things like logging trucks.
b) the horse I had as a teen was absolutely terrified of cars. It didn't deter me much, but I was young and stupid back then! Once, we met a large dump truck that was going really fast going downhill and my horse freaked. He dove into the ditch head first (steep ditch, at least 6 ft down), losing a shoe in the process as he spun around. I stayed on somehow, but when I think if what would have happened if he had going into the road instead, I shudder. Also, I was involved in a 15 car pileup a few years ago and since then, have a lot of anxiety about driving in bad conditions. I still do it because I have to and because I won't let it limit me, but that accident scare me badly. Not because of any severe injuries (I was fine), but because I had absolutely no control over the situation as I watched helplessly as cars slammed into cars over and over again (someone even slammed into the ambulance). I think my fear has as much to do with the cars themselves as they do with the horse. I do want my horse to be ok around cars, but don't expect him to be completely non-reactive to a huge logging truck flying down the hill. I don't even like walking on the road because of those trucks. So I would not want to ride him on the road a lot and will be choosing alternate roots whenever possible.
c) will try working him when we get back to the barn and tying him to a tree until he settles down. Thanks for the great suggestions!