Two people... two hours..? Somethings not right. I'm on my third coach and all the screens have come out the same way. Open the window, slide the screen out of the side track, push the top edge up into the top track and remove the bottom edge from the lower track... reverse the procedure to reinstall... EZ..PZ On a vertical install it's basically the same procedure... open the window, slide screen up from the bottom track, push left (or right depending on the install) edge into the track and remove the other side.
Now some spring clips might be stronger then others and there could also be a build up of 'gunk' in one track or the other... but a good cleaning after removal should allow for an easy reinstall.