There are a number of good suggestions above.

If I were in your place I would want to understand why she wants / feel she needs the full 20 minutes before her class starts in the classroom without interruption. She might be territorial, she might find lecturing stressful and wants / needs the time to prepare.

You now seem to have a second problem that both you (from the fact that you are posting) and her are upset. At this point I would learn if there is a departmental guideline on when you should be out of the classroom, or if there is no guildline then with the knowledge be non-confrontational, say you don't understand, and ask her to explain why she wants/needs all of the 20 minutes. Be ready for her to be hostile but listen first, then explain why you would like to have time after the class. Again she may be hostile to your explanation.

Once you understand you can decide what to do next.

There is an good book called "Getting to Yes: Negotiating Agreement Without Giving In" by by Roger Fisher, William L. Ury, and Bruce Patton. Which is a good read.  

Another instructor is pushing me out of the classroom right after my class ends
I mean, there are people who can't sing melodies correctly but they are able to play the guitar perfectly. Will such person be able to play the trumpet? When you hit the note on the trumpet do you have to worry about the correctness of the note or trumpet does it for you? I play the guitar, I even sing sometimes but I'm worried, will my musical hearing be good enough for the trumpet? Hope I made myself clear.
