How can I make my old dog comfortable with my new dog?

We have had a dog for three years. He is not yet neutered, but has an appointment next week. He is perfectly fine around our two cats and all humans, and 95% of other dogs. He is part Chihuahua and I honestly forget what he is mixed with, but he definitely looks like the small Taco-Bell dog, but he is a little bigger. (maybe 15–20lbs.) He lived with his brother for two years and they got along fine. My fiance’s mother couldn’t handle two dogs anymore and gave one to us, and he has been fine with us for the last year. The other day, I went down to the shelter and got a bull terrier / German Shepherd mix puppy about 8 weeks old. She is a female. As soon as we brought her into the house, my old dog refused to quit barking, and when we tried to slowly get the two together, my old dog bit my new puppy on the nose. It seems like it is a territorial thing, or possible intimidation because the new puppy of 8 months old is already bigger than the 3-year old. What can I do to get my old dog to settle down? The new dog is totally calm, does not fight back, and does not bark or growl at my old dog. Any help would be appreciated. I know the neutering should calm down my old dog, but will it be enough?