I realise that giving her the stick only reinforces the issue, but in that situation, it becomes a necessity. Not great!
It is good that you realize that she has learned that bad behavior gets her what she wants. But it is certainly not a necessity, and you must be in charge. Stop all play immediately and make sure she understands why.
This is the age when they start to challenge you. If you give in now, you are setting yourself up for big problems later on that you will have to undo, and that is much more difficult than nipping the thing in the bud from the beginning.
Hans would do anything for the ball. He loves those things more than anything. When it is playtime, I tuck them under my arm and head out with him on a long lead.
Lately, he had started get too excited, then to try and jump up and steal them from me. Once he pinched my arm pretty badly in doing this. All it took was a very stern, "Ah-ah, NO snatching!" and an about face back into the house. The balls got put away and I ignored him for a while.
I had to do this a few times, but he quickly learned that rude behavior meant playtime was immediately over
. Now I can tell he still wants to steal the balls, but all I have to do is give him a look and say, "No snatching!" and he knows.