Who is in Charge?
When you have a Shih Tzu and another dog, there will be a process of the dogs trying to figure out who is in charge (in other words, who is the Alpha Dog"). This becomes slightly complicated. You, as the dogs' owner, are the true Alpha Dog. You must show that you are the leader of both dogs. This is done by properly training your dogs to listen to you and take commands. You are the leader of the "family pack".
Aside from that, in a smaller socialization circle, the dogs themselves with need to know which dog is in charge of the "canine pack".
Most of the time, the dogs will be able to decide this among themselves. It is not always the dog of larger size that is the boss. Most of the time, it is the older dog that will be the leader. It is perfectly fine for 1 dog to be the leader and this does not mean that your Shih Tzu cannot be friends with another dog.
How do you know which dog is the leader? It will be the dog that goes out of the door first when you call for them to take a walk. It will be the dog that heads into the kitchen first when it is dinnertime.
It is completely natural for the older dog to discipline the younger dog. It is not acceptable if strong aggression is shown and the younger dog is injured. However, for the home to run smoothly, you should allow the older dog to "put the younger dog in his place" as long as there is no aggression. For example, an older dog may push the younger dog away if he gets too close to his toys.
Once you notice who is acting as the "Alpha Dog", you can help both dogs get along better. How? When dogs do not understand their place, it is very stressful for them. The pressure of trying to maintain their role as leader is hard work! You can help by giving the leading dog his food first. When you are giving out treats, give a dog treat to the "Alpha Dog" first. Doing this each day, will help the dogs understand which role they play and will make them happier dogs.