Tiny and Biggy - 1

I know 2 little girls, just a few months apart.. Lets call them Tiny and Biggy. Thats how these two are..
Tiny and Biggy are in the same age group - 2-3 years old, so they like to play together.. But Biggy is a little dominating, i.e. she wants everything for herself, wouldnt listen to anyone, and its her way or no way .. She shouts, cries when it doesnt happen her way, and at times hits or scratches the person trying to restrain her.. irrespective of who it is.. Tiny is towards the silent end, she does want things for herself, but she would share as well.. when things doesnt happen her way, she cries a lot, but then a distraction helps to get her attention somewhere else. She is afraid of strangers as well..
So when Tiny and Biggy play - there has to be a supervisor, so that Biggy doesnt start hitting Tiny. But then, Tiny wants to play where Biggy is and so does Biggy.. Whatever Biggy is playing with, Tiny wants to play exactly the same thing, and vice versa.. Initially, Biggy dominated the scene, she would not allow Tiny to play in her house, hide all the playthings, hit Tiny when she felt like and then Tiny would cry.. As time passed by, Tiny started retaliating.. If Biggy hit her, she would hit back, if Biggy came to her place, Tiny would hide her playthings..
Yet, both of them need to play with each other.. But little Tiny's Dadda is worried.. "Is she turning into Biggy? Lets not let her play with Biggy" But Tiny's Mumma says, She is going to learn a lot more things when she goes to school with several other Tinys, Biggys, etc.. Let Tiny decide for herself whats right whats wrong.. and Instead of preventing her playing with Biggy, efforts should be put on letting Tiny know what she should not learn..
I agree with Mumma..
I like to play with both of them.. Tiny is wonderful! Biggy can be cranky at times, but when she is not, she is a nice girl..