She was mostly likely just trying to move her. Some cats don't have the 'know how' to do what is needed. I had a cat years ago that was an amazing mum overall but she too couldn't figure out how to pick up the kittens and every time she tried they would squeal because she just couldn't get them right.

We are different from mum cat...we smell different & feel different & handle the kittens differently so, the kittens feel things are 'not right' strange, so then tend to cry out to let us and mum know something isn't right & they are uncomfortable or scared about it.

If Princess had an issue with you being with her baby she would not walk away from her when you went near. She would do just as she does with your sister. Princess can sense your sister doesn't like the kitten or is nervous around her and therefore has the instinct to protect her baby. She feels no threat from you so she is comfortable leaving you with her baby cause she feels her baby will be safe with you.