@layman,
No. You
think you understand but you actually don't, and until you come to terms with that, you will make zero progress.
The thing with inertial frames of reference is: none of your examples (trains, planes, rockets, cities) ACTUALLY represent or offer the basis for one. They are all very imperfect examples. A real train never ever is inertial. You can always feel that you're moving even with your eyes closed, simply by the balancing of the train car, the breaking, the accelerations, the turning... Likewise, and even if we can't feel it, a train station is circling around the earth center of mass, and revolving in a much broader ellipse around the sun, so it does not offer an inertial frame of reference either. These are just examples given to kids so they can vaguely get the ideas behind relativity. They are not
serious examples of inertial frames.
The other thing is: whereas an inertial frame of reference is required to compute the SR equations for all sorts of stuff, this frame can be used to calculate many things happening EVEN TO NON-INERTIAL OBJECTS. Ie the time dilatation of a clock in a plane flying around earth as compared to a clock left at the airport can very well be calculated accurately in SR, using an inertial reference frame. This is in spite of the fact that
neither the plane itself nor the airport are inertial. So we cannot use a frame centered on the plane, or centered on the airport, to calculate time dilatation. But if the experiments lasts only for a few hours, one can neglect the earth revolution and use a geocentric frame for this problem, with axes pointing at specific stars. That is to say a frame centered on earth but not rotating with earth. If the experiment lasts for more than a few days, one might have to use a sun-centric frame because the earth's trajectory cannot be considered inertial over more than a few days: it is in fact 'accelerated' by the sun's gravity into an ellipse, not a straight line.
Bottom line is: as far as we know, SR seems to predict all sorts of phenomena rather well. It's not a perfect theory by any means, but no amount of uninformed, confused blah-blah will tear it apart.