Not sure what your personality is around the house DK. It could be that your dog is afraid of you. When he pee's, I'm pretty sure that its a sign of submission to the alpha of the family.
I do not trust him at all. Just a few minutes ago, he was lying on the rug and started gagging and then threw up all over the brand new rug that we put in as I scolled him he peed on the rug.
No offense meant, but why would you scold the dog for getting sick?
When we take him out to walk, he usually pees right away but, when he has to do the other he will walk back and forth a dozen or so times. By back and forth I mean in a small six foot or so straight line. Back and forth and then he will do his business.
This is normal.
Only thing that I could suggest is crate training. Normally you would do this when the dog was still a pup. By not doing so it will make it much harder. The dog will normally not mess where it sleeps unless it is sick.
If you do this now, I think that you are going to have a hell of a time. You are going to have to put up with a lot of whining from the dog, and you are going to have a hell of a time even getting him to go into the crate. You cant get mad at this. You have to train him without getting mad. Even if it takes you 20 min's to get him into a crate, once you do get him in praise him and give him a reward/treat. Good dog.
As soon as you take him out, take him straight outside and wait for him to do his business, then praise him again. Good dog.
Scold him when he is out of the cage and chooses to do his business in the house, then put him outside for a bit. Bad dog, No!
If you and your family is not home, the dog is in the cage, when you go to bed, the dog is in the cage. As soon as you get home, put him out. While you are home, allow him out, but if he does something wrong, command him back in the cage.
After a while, you will be able to command him back into the cage and leave the door open, he will stay until you allow him out. Use the command BED, or something else that is simple for him to learn.
He will be reluctant, but after a while he will get used to it.
You seem to have another problem though. Your dog is terrified of you. It recognizes your anger and I would guess that there are times that you are not raising your voice in anger towards the dog but towards someone/something else and the dog will pee.
All that this dog knows is that Alpha is angry, and it is scared to death that this anger will be turned on him. This is a tough one to overcome.
I have never in my life hit my dog with my hand. If she did something that was so bad that it warranted physical punishment because she kept doing it/not listening at all, I would grab a pillow off the couch. I never hurt her, just made sure that she understood that I was alpha. (better treatment than they get in the wild)
She is very well trained now. I rarely even have to raise my voice to her, I just say NO. But, when I get pissed at something and raise my voice, or swear in anger, even though it is in no way directed towards her, she will do the same thing that your dog does. She will start shaking like a leaf pee on the floor, and do what she can to stay away from me.
Really makes me feel bad, lol, I have to tell her its ok, good dog. She does not understand that it is not her that I was angry at, she only knows that I was angry.
For jumping, a knee to the chest as he jumps. Not hard, just enough to push him back.
Barking is also a tough one. Have you tried one of the anti bark collars?
I hate to tell you this, but unless your dog is really not mentally all there which I guess is possible, the dog cannot be blamed for its actions. From what I can understand through training and talking to trainers is that 99% of the time it is the fault of the owner. You have to be willing to take the time and possibly change your approach, but you can train this dog.
Something that I would advise is to go and talk to a trainer. If you can find a good one you will be AMAZED at what they can accomplish.
You said that your family still loves him, but do you? Even with his faults are you willing to try anything in order to keep this pet a part of your family?