First, this is not jealousy or any of the other human emotions you may want to ascribe to this behavior. This is a dog who is still new in a home and who perhaps was not entirely housetrained in the last place he lived. You need to stop thinking of this as being a deliberate thing and instead treat it like a training issue. If you put human emotions onto a dog it never helps and is often of great detriment to the dog.
First, clean everywhere he has peed with a special enzymatic cleaner designed to neutralize the odor from dog pee. You cannot do that with regular cleansers or vinegar or anything else. Even if you cannot smell it, the dog can unless you ude the right products to remove all of the smell.
If the dog doesn't do any business when outside, bring him back in again and watch him closely, not taking your eyes off him, and if it looks as if he's going to pee somewhere, hustle him outside (gently, NO scolding, nothing harsh), and then praise him when he pees outside. If he doesn't seem to be going to pee in the house, wait 5 minutes and take him out again. Repeat until he pees and praise him and give him a treat.
Take him outside often. Once an hour at first, and every time he does business outside you praise him and give hi a treat.
Basically treat this as if the dog were a little puppy who didn't know how to be housetrained. Do the basics, make sure you never scold or punish the dog for going in the house (that will only make him sneak off to do it when you can't see him), and be patient. He will catch on. Make sure, also, that this training is 100% consistent. Everyone who lives in the home must be on board with this approach or it will not be successful.
And I would never, ever recommend to someone to make their dog live outside, so I am glad that you wouldn't do that.