Oh my. Yorkies. Having owned a Yorkie for 16 1/2 years, you must know that I am very well trained. Yorkies are much smarter than humans, as you are learning. They start our training as soon as they hit the doorstep, and it continues until you bend to their will. Now, Mr. K9-Lovers and I are so well trained, that we don't even question the commands any more, we just listen and obey.
Yes, you need to be with them when they are outside, even in a CYV. There are large birds who will take your babies away. We have solved the problem by installing a doggie door panel into our sliding glass door that goes out to our lanai/birdcage. There is a grass area inside the birdcage that is the potty place. That way, the dog is protected from birds of prey by the birdcage.
If you don't have a grass area inside your cage or lanai, an easy fix is to make a raised bed like you would for a garden, plop in some dirt and grass seed, and voila -- potty place. You can build it atop of concrete, and if it is under a solid roof, be sure to water. You can use one layer of bricks or garden edging stones to enclose the dirt. You might even want to put the dirt in one of those large plastic trays that are meant to catch leaks from a washing machine (find them in Lowes/HmDepot near the washing machines or hot water tanks). That would keep any dirt from washing out from under the bricks. Then, for your little boy, just put a stick in the middle of the potty place.
Another idea is a portable "loo" for dogs. Just google "indoor loo dog" and you will see all kinds of ideas.
Gotta love those bossy little Yorkies. My boy watches television -- tell me a funny story about yours . . .