Bamster, I disagree. Alpha dogs always assert themselves by being Number 1. They get their food first, they get the most love, they are petted first, their name is called first, they exit the room first, etc. etc. By giving more individual time to the shy dog and babying him, the original poster would be confusing both of her dogs, causing more uproar. The shy dog is clearly a submissive boy. By giving him the resources first, the JRT is terribly confused and wants to assert herself as Alpha. That'll cause unnecessary scuffles.

One of my theories is that the JRT senses that the other dog is half blind (read: weak). In pack hierarchy, the weakest dog is often picked on. If this is true, I highly recommend speaking with a dog behaviorist and see what the best course of action is.