Two dogs aggressively fighting?

We had two dogs in our house, a chihuahua and a apoo. The chihuahua is by far the alpha. We ahve just adopted a new rat terrier/chihuahua mix. The chihuahua, Tito, and the mix, Toby, seem to be fighting for the Alpha role. Tito and Toby have been aggresively fighting each other, but Tito seems to be submissive to Toby. We know that they will never get along unless Tito is the Alpha. Tito has mounted Toby, and he didn't mind, but after that Toby started, like, sniffing and softly biting Tito's neck. We are SO confused! Our apoo has nothing to do with it, we doesn't really care who's alpha. We don't know what to do to make sure they don't fight anymore because my sister has already gotten bit by pulling them apart and we are afraid that our one year old could get in the middle and be severely injured.