N.J.
Dear Sam,
You really have a dilemma on your hands. On the one hand, my daughter tends to order her friends about telling them exactly what to say and do. But, she's a very logical child and likes things done in a certain way. There is not a creative bone in her body. Her best friend is pure creativity, no logic and seems to thrive on the structure my daughter provides, so the friendship works well.
I think your daughter's friend sounds very insecure. I wonder how many other children at school play with her or if she has any other friends? Threatening your daughter with the loss of her friendship is not nice and its something you need to speak to her mother about. Just be honest and explain that you hesitate planning a play date because of all the drama that ensues with these threats.
Is she showing signs of being a bully? I don't know, but if your daughter likes playing with this little girl then let them play. Just have the play dates at your house where you can closely supervise or ask the mom to meet you at the park.
I think you need to really watch these two kids play and see if its truly one-sided. I hated teaching first grade because of all the drama, I didn't realize the drama started so young, but it does. I don't think its a question of interfering, its your job to. Little girls need guidance and they need to be shown how to solve problems. Next time your daughter does not want to be the kitty, you need to be there to say, "how about we take turns choosing the game" or "okay Anna you be the kitty for five minutes, then when the timer goes off its Susy's turn to be the kitty."
Teach your daughter now how to deal with a difficult friend. In elementary school she'll need to be able to solve problems on her own and nobody wants their child to be a push-over.
Just keep saying to yourself....this too shall pass.
~N.