Something is just not right with this picture. Have you taken him back to the vet to see if he has any other issues going on? Nobody can tell you not to give away a dog that is acting aggressive toward your family. If he had never acted this way before I would take in to the vet before you do anything else. Have him check out for a medical issue. If he is attacking and biting, keep his leash on him at all times. That way you can control him without getting bit again. It is not fun to be bitten by any dog I don't care how small. I would also agree not to use a shock collar when a leash will be just as good for control. Probably even better.
I would like to know when he is attacking? You mentioned that he did it when the cat jumped onto the bed. That sounds like territorial behavior. I would NOT let him onto the bed it he does this. Once again, if you have a leash on him and want him to get down and are afraid of being bit you can control him with the leash. I would not attach it to a collar but leave him in his harness, you do not want to damage his trachea. Plus if he is totally out of control you will not hurt him if you need to pick him up by lifting with the harness. Never pull or use force on their necks.
Working with a good trainer is an excellent idea. If all else fails please surrender to a reputable yorkie rescue. There is always help with this type of behavior and a rescue would be willing to work to help address this issue.
__________________ “Never argue with a fool, onlookers may not be able to tell the difference.”  Mark Twain |