Where are you at with boundaries? Does she know what you will or will not tolerate?
Have you asked her if she wants to see other people? You cant avoid this. She needs to know that you feel this is unacceptable. If she wants to date then you will have to figure out what that means for you. I would tell her that if she is seeing someone else then she needs to move out. Sounds like you need to take back the reigns.
That is my Opinion anyway. Others may disagree.
I let me X walk all over me. Lie to my face. Tried to be the nice guy. Where did that get me.