I see where you're coming from - I had something like this happen to me once where I was asked to make cold calls to customers to sell a particular warranty because our company had lost the person who filled that job. I was really upset, because I hated it and felt undervalued in my current position.
That being said, I buckled down and became the best damn cold call-warranty seller I could be. In the end, I got in the good books with my managers and boss, was thanked for being such a team player in the company, and ultimately learned a lot about a different department. I ended up with a PROMOTION at the end of it because my boss appreciated my team attitude and my ability to take on new tasks with a short learning curve.
My suggestion - suck it up, help out the team, and put a big old smile on your face when she is around. If this woman has as long of a leash as you say she does, I'm sure it's not beyond her realm to make suggestions of employees that should be let go. The last thing you want is to be known for a bad attitude and get less consideration in the future.