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It's easier if you rewrite the sentence like so:

их владельцы старались его не пускать на чемоданы.

их владельцы ( Their owners ie. of the suircases) старались его не пускать (were trying not...

With a bit of guesswork :

1. then it could only take them as far as the tube, which was already shut.

2. Why had her father-in-law still not mended his car and why hadn't he rolled it right up...