Nine weeks is really young, and the YTCA requires breeders to keep pups a minimum of 12 weeks. Even though the pups are weaned, the mother teaches other important socialization skills such as "pressure of bite." Remember those little baby teeth are sharp and your dog may just be doing what the mama would have done if given a chance. Whether your dog can do what the mama would do, remains to be seen, but I do think how you react to it is important, and the puppy should learn his place in the family is under the other dog. He will probably learn to submit without too much provoking if you don't interfere. On the other hand if the first dog really is aggressive, I think you need more advise than I can offer. This site has some information on the 12 week rule and Maltese, it would apply to the yorkie as well.
Why do Maltese puppies need to be 12 weeks old before going to a new home??
Here's a quote from the link:
"Maltese puppies learn some valuable lessons in the weeks after weaning, including how to get along with other dogs, and that biting hurts. These are lessons, all learned in puppy play, that no dog should be without. Some of the most important lessons in life, a puppy will learn from it's mom and siblings. They NEED this time with their mom and littermates!!"
So it's probably a good thing you have another dog.