I was hoping you were still online but let me get you an answer so it is waiting for you when you get back online.
You should definitely reintroduce the dogs away from home. If possible, choose an area such as an enlcosed tennis court where they can trail their leashes and interact more normally without being around other dogs and people but still able to flee from the other if necessary.
You don't want to be holding the leashes as often an owner will worry a little about the dogs reaction and the dog will pick up the owners worry through the leash and then think the other dog is the cause for your worry and be protective of you. This can set the dogs up to fail which you don't want. If your dog has been the aggressor, you might want to get there after the other dog is already there and at the far side of the court.
Keeping the leash attached will allow you to grab or step on the leashes to control the dogs if they do get into a fight. I also what you to pay attention to body language as well since it will help you determine whether the dogs are feeling friendly, aggressive or dominant. The following sites are helpful with learning body language.
You will also need to involve the yorkie in the meeting with the new dog as well. The Yorkie may end up being the most dominant of the dogs since the other dogs are elderly and he is likely still in good health. If you feel you will be too nervous, perhaps you have someone else that can help bring the dog into the meeting place without worrying as well.
I would take some tasty treats like hot dog slivers and if the dogs ignore each other, you can give your dogs a treat. If the dogs are interacting well, you can call each of them to their owner and give them a treat away from each other so food aggression does not occur along with nice calm praise. If they show any aggression toward one another, I would give the leash a tub and deliver a firm low toned "NO" as a reprimand. You can even correct any aggressive body language you see as well.
I'd try for several meetings away for home before inviting one to the other's home. Before the meetings, take a towel and rub it all over the dogs in one household. Have your friend do the same, then exchange towels so each dog is more used to the other dog's scent. That way when they meet, they already know the scent. They likely have already smelled it on you and your friend, but getting them more familiar with it usually helps.
Once you actually do the meeting, I'm sure you will have more questions, so even after rating this answer, you can come back for further clarification and help at no additional cost.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer so I am compensated for my time.