What can I do with an overly submissive dog?

Train him and give him self esteem. get him enrolled in obediace to get use to toher dogs and training.

I had to keep my sister's city dog, also a male JRT. He was spoiled and acted very much the same way at first. I threatened to turn him into a "hound dog" which only meant I took him outside and treated him like a dog and allowed him to run, play and explore all he wanted. (We live in the country on a farm) He soon began to eagerly await going outside with me, became more assertive, and absolutely trembled with excitement to see me put my shoes on. When my sister eventually came to claim him and take him home a few months later, she called me trying to find out what I'd done to her dog. He moped and mourned for his new hound dog life, and he even quit eating for awhile till he finally readjusted to living with her again. Anyway, point is, show this fellow how much fun it is to be a "hound dog" and you will find he'll make a beautiful turn around. JRT's are naturally curious and don't really understand their small size limits them. Give him a chance to develop his character and he may surprise both of you!

Professional training is needed and please, he is an animal.

Well I would stop touching this dog you say you have stopped talking and that has helped. Look go outside and teach him a hand touch present the hand and when he touches it give a treat on the hand and repeat soon you will have a hand that your dog will want to touch and you can now us it as a recall or a way to guide your dog to where you need him to go. Next I would teach the collar grab game it is basically touch his collar give a treat touch his collar give a treat over the week now touch his collar and slowly guide the dog with his collar to move forward an inch give a treat. If he tries to tuck and roll you have gone to far to fast.
Next all his food comes from your hand use it for these simple games and teach him you are the one that is the greatest feeding one piece at a time. I would also change his name I would bet his name is poisoned I would bet someone has said his name in anger and with a correction this dog wont come to a name that he knows it has been used to later give a correction like a shake or a rough time in his kennel. Change his name.
When you are at the transitions go outside the door and go behind the door so the dog doesn't have to pass you he has a clear run outside or better yet go outside and call him outside in a fun voice and show him you want to play play with your other dog he probably trusts your other dog. Jacks love to play tug games and you could help build this dog confidence back up by playing tug so find a stuffed animal and use it for a tug toy. You could also leave a short leash on him in the house so you have a bit more hands off the dog till he starts getting better.

I know some of this stuff sound real basic and all most dumb but give it all a try and I would bet within 2 weeks things will get better. Keep everything upbeat and fun do his training outside in different locations go on walks and runs, have him meet new people and kids give the new people treats and let them give him a treat and carry on to the next adventure. Jacks make awesome trick dogs and agility dogs enroll him in an agility class in my agility class I tell my students they can't use the word NO or any word or sound that even might be thought of as a negative not ah ah or oops nothing. Trust me the dogs still learn everything they work the entire hour long class and they don't shutdown or have submission problems. I would also hope you could remove the No and negatives in your home for a while and LOOK for times you can reward your dog or say YES when he is doing something you like even if it is something simple like going to his kennel or mat to lay down. Do fun stuff like clap your hands and give him a treat laugh and give him a treat act silly and give a treat run away from him and give him a treat get down on all fours and give him a treat you need to turn his dog around to being the terrier he was bred to be throw a ball and when he chases it say YES and be ready with a treat if he wont come back with that ball who cares have a second ball and throw it he will have to drop the first one and then you get it back trade him a treat for the ball never take something from him always trade with him. don't forget your dog has been corrected so often that for him he needed to act this way and it has worked for him. He tucks and turns you shy away because you don't want pee on you and you stop what you are doing. Now he could of also been the shyest puppy in the litter this could be his poor temperament he may never have been abused by anyone and you do have a dog that is very shy so keep that in mind I think it can be fixed but you will have to think first how not to do what in the past was a trigger for your dog to tuck and roll and pee. Good Luck

You're right, the sumissive urination response has been reinforced.
Try using more canine body language with him, the short article in the link may give you some easy pointers.
http://www.canis.no/rugaas/onearticle.php?artid=1

I think you are on the right track by ignoring the behaviour.. Unfortunately it sound like he has been trained to do this. How crazy is that? I can't believe that lady said to give him treats when he does it!

You should work a couple sessions a day on obedience training with him to try to raise his confidence. (including tricks or whatever) and occasionally throughout the day ask him to do some little action he knows how to do and praise him for it.... try to find opportunities to give him praise for things when he is not submissive rolling and urinating.
Do you mean he does better when he follows the GSD inside or out? If so you should try to build on that and have him follow the other dog. maybe that would make him more secure?

Poor Jack, it wasn't his fault at all. Whoever gave him treats when he did this should be blamed. He was actually encouraged to do it!

I tink this poor dog has been confused by the other people and he doesn't really know what is right and what is wrong, even he is almost one year old. Say no in a stern voice whenever you see him do this and continue to ignore.

Instead of just correcting him, perhaps you'll teach simple new things, eg come. When he does it praise him excessively so that he knows what it is like when you are pleased with the right things that he does. He needs to know the difference between good and bad.

Don't even raise your voice with this dog or else he will be so frightened that he might just shut off his communication with you as soon as you try to make a command. good luck!

Get the male doggie diapers. It DOES sound like his old owner reinforced his behavior with treats. I used to have a female pit bull that did the same thing. Got her as a pup. She was just very submissive.