You don't necessarily need to get a Yorkie with an unknown past from a "rescue" organization to give a Yorkie a home who finds itself without one. Neither of my two Yorkies was a "rescue" dog but both needed new homes. One Yorkie was 'advertised' on a homemade flyer on a break room table where I work and the other was in an internet "advertisement" but both were completely private 're-homes'...leaving the 'acquirer' [me, in my case...lol] to decide what's best under the circumstances. I am grown up enough to figure it out and I expect you are as well.
If you are not on a specific time line to get your second dog, or perhaps don't even care if it is a purebred Yorkie, Yorkie mix, etc., there are other possibilities including mentioning to your vet that you would be interested in an additional Yorkie needing a loving home to move into due to circumstances beyond its control.
I took two (2) cats when our friend found out she had pancreatic cancer, but as a backup, she had told her (our) vet that her cats would need homes soon, and he was prepared to help with finding them places to live...or even put them down humanely if necessary. After we took the cats to our house, we notified our vet, who changed ownership in his records to our name...she had notified our vet we had agreed to take them, but he was still holding open the possibility that anything could still go wrong, too.
Things do have a way of working out, and you are already investigating the possibilities. I'd not start to sweat the small stuff just yet.
