I've heard that puppies, like children, go through a period of sep anxiety and just general fear. Not sure if this is true but i know it happened with my Layla. It is really important that you praise him when he IS behaving. Also positive reinforcement- when he is behaving in the car- give him treats and praise. Make sure he is in a crate in the car- for safety reason and to give him a sense of comfort. You may have to back off a bit with other dogs if he is upset at the dog park- maybe just go up to one dog at a time and say hello- and if your pup is quiet and not barking- praise him and give him a treat.
Does he know sit? I find if Layla is misbehaving during a walk- i immediately put her into sit and hold her attention with a treat until the distraction has passed- give that a try