Jack russell toilet issues

Question
I have a 14 month old male neutered Jack Russell. We got him neutered at 7 months and he always had some issues with holding his bladder, sometimes its like he doesnt even know he's peeing as he dribbles all through the kitchen. He also is a submissive urination type of dog and also an excited urination type of dog. It is now escalating to excitement pooping if that makes sense. When its time to go for a car ride to the dog park he has deficated three times now in my car on the way to the dog park and this last time deficated in the house as I got the leash from downstairs and ran upstairs to get my coat. I have tried taking him out to pee and poop before we go to the park but even if he has a bowel movement before we leave he seems to still go in the car.
He can go in his crate all night and all day without making a mess but Im getting tired of cleaning up pee everday it seems. He goes out for a pee almost every 3-4 hours when Im home, sometimes more frequently then that. Its also hard to walk him as much right now because I am 9 months pregnant, I try a walk everyday but sometimes its a short 5-10 minute walk.. and going to the dog park or running in a field with our other dog 2-3 times a week.
What can I do, Im so tired of this dog and everyday I try to start over new but its getting too much now, our other dog doesnt ever do this, and shes still a pup

Answer
To clarify, did the dribbling "like he doesn't know he's peeing" begin before or after he was neutered? When you say the dog can hold it "all day and all night" in his crate, how long is the dog crated at one time?

I've never heard of "excitement defecation" (which doesn't mean it doesn't exist, I'm not experienced it or read about it), but have seen it as a fear response.

Many dogs don't enjoy car rides because it upsets their stomach, or they are anxious in the car for a variety of reasons. Your veterinarian can prescribe something to help with car-sickness. If your dog is anxious - some signs of anxiety are drooling, excessive panting, eyes wide, can't settle down/pacing.  Some dogs are helped by an Anxiety Cap or Anxiety Wrap (do a Google search for those products) and/or riding in their crate in the car.

How have you tried to correct the problem?