Shish Tzu's can be snappish. Did these dogs know each other before they came to be with you? Pomeranian's need proper introduction of new dogs. With both that said I would suggest you don't allow that behavior. Google nothing in life is free (NILIF) and start using the program. It is a gentle easy to implement routine that will help you show leadership. I would have the female checked by the Vet to be sure there is no pain or medical problem that is causing her to act as she does when you lift her. If all checks out medically then ignore her completely for a few days and then gently pet her and show her attention gradually until she is comfortable with being lifted. Some little dogs really do get scared when they are lifted so far off the ground. And they are new to your home, so be patient but don't coddle those little dogs, show love, but don't over do it and be sure that you initiate it. Your hybrid is a mix of two very protective and yappy breeds - when they bark at the door when visitors arrive be sure to show them that a couple of yaps is sufficient, thank you, go lay down now.
As for there playing I think they will learn to work it out, just don't let her get abusive with the other pup. Good luck.
