Sorry about the issue you have had with your Yorkie and your parrotlet.
Yorkies are Terriers and were bred to chase, find and kill prey. Although more domesticated and coddled, that prey drive is present in today’s Yorkies as well.
My little girl is sweet and cuddly but will chase every squirrel and cat that finds its way into her yard. When she was attacked by a hawk, she fought for her life (at 3.8 pounds) and killed the hawk.
She will play with another dog or cat, but if it gets rough or she feel threatened she will go into that prey mood.
Of course you don’t know for sure what happened to your bird I gather, but keeping other critters, that might be vulnerable, safe could be a chore around any Terrier.
__________________ .  Cali  , and Cali's keeper and staff, Jay No, not a "mini" Yorkie - She loves to motor in her Mini Cooper car |