Well, without having real experience with QC API, here is my contribute:
- The logic you are doing, is to create a session cookie with Chrome, then,
- Use this same cookie to send requests' requests ( :) )
I think you need to "fake" in requests the user-agent to be the same as Chrome. (I did this with Firefox some years ago)
I think you should not use the same connector (you are already connected). So there should be an alternative to not request the login form
(unless this is the correct URL meaning, "if user is not logged in, then show the form")
Good luck.