Sm chi wants to be alpha dog. Large dog want stand for it.?

Our chi got a long with large dog when he was a puppy. Now he is 3 yrs old and challanges large male dog. On 3 different accausions large dog his authority to the chi but, we had separated them before it got worst. Last time large dog had him by the head and was shaking him. When we finnaly got to him he was scared stiff I mean he was really stiff then he starting throwing up. We thought that would had finnally showed him his place . But, he growls at him at first sight. The large dog easily could have killed him but, didn't. Do you think its dangerous for them to get together or should I keep them apart. Or maybe get him fixed would that calm him down.