Yorkies that have had you all to their self will do that but with attention and lots of reassurance they come first it passes. It sounds like you are more interested in the puppy that the dog you have had for awhile. Larsson may feel that....
I would think if one had to go it would be the new puppy not the one you have had and loved for along time. It doesn't make sense to get rid of a dog you have loved for along time for a new puppy as the puppy will grow up eventually.