We can understand how difficult this must be. We believe that you are correct that the shelter did not tell you all... however, they may not have known.
We have seen this before; chances are that your Yorkie was abused and/or neglected by an older gentleman. What he may have endured could even have caused him to develop PTSD. This can and does happen (about 5% of military dogs suffer from this).
Canines are able to group humans by gender, height, scent, even hair color. As you probably know, canines have excellent long-term memory. The past is not forgotten. And your father, unfortunately, may remind your Yorkie of terrible events.
There are some things that you can do. Though, with your father being 73, we are not sure if this will present any difficulties. In addition, since you have other dogs and we are not sure of how things are done with them, this as well may present a problem.
You may want to make the following advice is a rule for all of the dogs in the house, as this can only bring about positive results no matter the dog.
The two main issues to work on are: Respect and consequences.
Respect: No matter this Yorkie's history, he must learn that your father is to be respected. For a dog to respect a human, he must see that human as his Alpha. Being an Alpha involves very fair treatment and a mutual respect with an appropriate human to dog relationship... So, no doubt your Yorkie did not receive this from his previous owner. This will be new to him. So, not only will this help resolve the issue, but it will also help your Yorkie separate his previous owner and your father as two distinct individuals.
While giving treats for good behavior is indeed an important aspect of teaching a dog right from wrong, in cases of severe behavioral issues such as being aggressive, consequences must be given as well.
To bring about changes in regard to both of these elements, we recommend the following (and again, you may need to do this well all of your dogs, which will have no ill effects):
Any food, even a small treat, is NEVER given until the dog obeys the 'Sit' command. Your father should be the one to command a 'Sit'. If your Yorkie/other dogs do not yet know this command, start training immediately. All bowls should be placed up high on a counter. The dog is commanded to 'Sit'. Once he obeys and is remaining in place, your father places the bowl down.
Any snacks are given in the same way. Dogs know that food equals survival and ensuring that a dog 100% fully understands who is responsible for keeping them alive creates a huge sense of respect.
While this may not be applicable to your situation, any time that your father would leave the house with your Yorkie, he enters and exits first. The Alpha always enters/exits the den first.
For now and until this resolves, this Yorkie (and for practical purposes, all dogs) should always be physically lower than his humans. If the dog is on the floor, humans need to be sitting or standing. No one should be sitting on the floor with him. And to maintain this physical authority, the Yorkie should not be allowed to be up on the sofa or on a human's bed.
For consequences. It is vitally important that you have a canine playpen
or small gated off area for time outs. A separate room will not work. This needs to be an area in which the dog can see the family but feels ostracized, albeit temporarily.
The very moment that this Yorkie growls, snaps at or gosh-forbid goes for a bite, he is to be immediately placed for a time-out. No words should be spoken to him. No eye contact should be made. The rest of the family should behave as if he is, by all accounts, completely invisible. If needed, remove the other dogs to another room or have someone take them outside, etc. so that your Yorkie receives ZERO interaction.
All dogs see the world like this: Within the pack (family of humans and pets) that live in the den (the house) there are Alphas (human leaders) and Betas (animals). If a dog believes that he did something so wrong that his pack turns their back on him, he will seriously re-think his actions.
So, immediate banishment is needed. Be careful even about what you say to each other during this time, so that the Yorkie does not mistakenly believe that he is being spoken to.
How long a time out lasts depends on at which point a Yorkie notices that he is being ignored. This can vary from 5 minutes to 20 minutes. Once you (from the corner of your eye) sense that he is distressed about this, allow 5 minutes to pass.
Then, release will be conditional. Bring the Yorkie back to whatever positioning he was in at the moment that he acted aggressively. For example, if your father was crossing the living room and stooped to pick up a paper when the Yorkie tried to bite him, have him repeat that action. See what the Yorkie does.
If he is aggressive again, immediately banish him by following the previous advice. When it is time, repeat the conditional release.
When a dog is aggressive like this and has actually bitten people, it may take anywhere from 4 to 5 cycles of banishment/conditional release per day and up to 2 weeks in total; however, he will learn that aggressive behavior has no place in the den (house). And trust us, there is no dog that willingly and voluntarily strikes out on his own, not wanting to be part of the pack.
To summarize, the aspects of teaching respect via food (and entering/exiting), authority via physical positioning, and teaching that growling or attacking your father will not be tolerated should all come together to bring peace and a better understanding to this Yorkie.
In fact, dogs that act out like this are certainly not happy dogs. Feeling tension, stress and spikes of adrenaline severely impact a dog's ability to enjoy life. Once this training is complete, he should be a much happier, more well-adjusted dog.
A word of caution:
When a dog snaps, bites and/or draws blood, this should never be taken lightly. You will need to decide if training through this is safe for your family members. Especially when it comes to young children and seniors, feel no shame if you decide that the risk of more bites (before training is complete) is not a risk you are willing to take.
Some cases warrant bringing in professional help. You may want to consider hiring a professional canine trainer for one-on-one sessions that take place in your home.