It's easy to train your dogs to use a doggy door.
With one person on each side of the doggy door (requires 2 people), one person holds the dog facing the door. The person on the other side calls the dog. The person with the dog holds the door open so that the dog can see out the other side. With a gentle nudge, push the dog through the door to the other side. The person on the receiving end praises the dog and gives a treat. Now, reverse the process, always rewarding and treating. After a few times of this, barely push the door open so that your dog feels the sensation of the door on his/her head and back. Do this a few more times with praise and treats. Now for the big test. Try it again without holding the door at all and see if your dog goes through on it's own. In my experience, it only takes one or two training sessions and your dog will catch on and be glad to use the new-found freedom.
Since you have a Yorkie (very smart little dog!) then you should have no problems. Don't get a larger door than necessary, get one that is just a tad higher than the height of your dog's shoulders. A dog will lower it's head and take most of the door flap weight on it's back.