There is a saying in business - "learn to manage your manager". In this case, learning to manage this woman you are describing is in your best interest. I imagine she reads how you feel about her. Finding a way to be an ally rather than a foe is in your best interest. Doesn't mean you have to like her or even suck up - just treat her respectfully (I know, this won't be easy ... I had to learn this the hard way).

Once you've cooled things off with her, when she drops off some stuff on your desk that you don't rightfully own, you could say something like 'whoa, wait a minute, I am on the such and such project and giving that my full attention" and she might actually hear you.

Best wishes - resentment is no way to live.