I think the logic behind the post is quite confusing. You should tell your students directly that discussion can only happen during office hour, and mention that there is another class afterwards. And you can extend your office hour (in a different day, say) by some period of time or move it if you wish, this can always be discussed with department secretary. 

You suggested that:


  Many times in the past I had a similar situation and never had any
  issues with it.


as well as


  In my evaluations the fact that there are always several students
  approaching me with questions after class considered as very positive,
  meaning that students find me approachable.


and many other reasons claiming your behavior is tolerable and okay by your standards. But these justifications is simply not related to the fact that she finds it uncomfortable because you did not end up the class on time. Since you are aware of that, you should do something concrete to resolve this issue. For example you can cover more background in the lecture time available, and encourage students to come to your office hour for longer 1-1 discussions. 

My impression for after class discussions is totally opposite to yours; the fact students coming after you after class usually means you did not explain the material well enough during class or unclear during the grading process. Your course should be in the format like "Calculus III, 2:00-3:00pm, Room 31A, Darwin building". If the description did not mention an extra 15 minutes for afterclass discussion, then it means you do not have it. As what the other instructor does when she comes to your classroom is totally irrelevant. In my experience a student (not even an instructor or dept chair) can knock at your classroom door and friendly to ask you get out without giving any specific reasons. They might need the room for group projects or whatever. The fact you are late should be compelling evidence against you already. 

You also suggested that


  Last time the instructor told me in front of my students that I don't
  understand "simple things" and that I am "playing games". When I was
  talking to one of my students, she stood very close to us and clearly
  demonstrated that she wanted us out. I tried to explain her that I
  couldn't go anywhere else due to my time constraints, but she didn't
  want to listen to me. I really don't understand what "simple" things
  she meant and what "games" I am playing.


I think you should think from her point of view, that your class should end up on time. The fact that you have time constraints, etc is irrelevant to her. If you think these are legitimate reasons to justify your behavior, to her you were simply being immature and using poor excuses. You may have your disagreement and ask for support from senior faculty in the department as Prof. Clark suggested, but her position is very clear. If she demonstrated you need to get out, then you need to get out even if this is the final exam. Unless you have a student with disability that needs extra time, etc I think there is no point arguing further on this issue. 

Another instructor is pushing me out of the classroom right after my class ends
I have an external HD with USB 3.0 and a laptop with a USB 3.0 port. Can I connect the two safely to transfer data and watch films stored on the HD for instance? If so where can I buy such a cable to do so?
