Start to crate train your Jack Russell. Make the crate be a bad place not a safe place. Put him in there for a time out when he is too hyper/being mean to the other dog/ barking at the other dog/ basically whenever you think his behavior is not appropriate. Make him know he is being bad and continue putting him in there for five min at a time. If he is winning and/or barking in the crate, cover the crate over with a blanket which should stop the barking.

Also when feeding, treating, and giving attention always do it first to the shy dog and second to the jack.. and only give that food/treat/attention to the jack if it is being good and not being resentful of the other one by barking or biting.

After awhile the behavior should stop/fade away using these methods once the jack knows that his behavior will not be tolerated and the time out he gets would be a good time to work on getting the shy one to come out and play and give it some quality loving time.

After you do this for awhile another thing that will help is when you watch tv sit down and put one dog on each side of you petting both of them simultaneously.