2 yr old desiring family members not to talk

My granddaughter just turned 2.  She is bright and articulate and always interested in new things and how they work, etc.
She has a very independent attitude and her favorite expression is "Emmy Do!".  When she gets tired or cranky, the first behavior she exhibits is to DEMAND that any person in the room (except her mother and father) not talk to her and then demands that they leave the room.  She stays with her other grandparents 4 days a week, is partial to her grandfather and makes the grandmother leave the room, which she does.  When she does that with me, I try to tell her I am going to do something else and come and see me when she wants to talk.  Sometimes, when I am comfortable she gets upset when I wont go and will cover her eyes and move swiftly on to a tantrum.  I have never seen this particular behavior.  What is she trying to communicate and why.

thank you

[Kevin Kennedy, Ph.D.]

Children this age are famous for wanting to exert their influence - they are developing more and morer mastery as they mature. However, while this process is normal, it does not imply that the adults around her should necessarily accommodate her wishes. I suggest it is a mistake, in general anyway, for the adults to be lettting her 'call the shots' about who is and is not going to be present in a room. The adults have to exercise their judgment about when and how to defer to her wishes. It sounds to me like you are going overboard to accommodate her. Handling frustration is a normal part of life and it's perfectly OK for the adults to make decisions she will not prefer.

[pd78]

Thanks so much.  It is reassuring to get a physician's input into what the behavior means.
I am sure I will be back when she is 3 or 4.