Any ideas on how to introduce these dogs?

[Nelly]

We have a 3 year old pekinese pomeranian dog named Bandit who is not exactly a family dog. He is more of a one person territorial dog. hes my mothers dog. But he takes it to the extreme, he's always up her ass and howls and whines when he cant be. Hes kind of vicious around little kids and people he doesnt like. and growls at me and my brother at times if we get more attention from my mom then he does. Hes very vocal growls and everyone and everything and constantly barks all the time at the littlest noises. When we try to dicipline him for what he does wrong he shows teeth and snaps. We do already have a cat that he doesnt mind being around at all because we had her first before he got here. Shes usually the one picking on him. We also had a stafordshire terrior/ pitbull mix who was 3 years old when we got Bandit. As Bandit grew up around him they created a very strong friendship. Although Bandit thought he was above this dog and was always picking on him. We had to put the 3 year old pit mix down because he was sick in june. and after that bandit became way more possesive of my mother and alot more vicious. My mom also doesnt discipline him the way she should or train him the way she needs to. She kind of brushes off the bad things he does. Any way we got a new dog and hes a 10 month old pitbull/ ridgeback mix. And bandit bullys him, attacks him, and wants nothing to do with him. The new dog is petrified of him. We tried having them meet outside before bringing the new dog in the house and it didnt work. How can we introduce the dogs so they can get along?