Is it permissible to shorten prayers (qasr) in Dubai or Amman, knowing that the questioner works in Amman and travels weekly between it and Dubai, where his family resides?

The mentioned distance is considered a distance that permits qasr (shortening prayers). It is permissible to avail the concessions of travel, such as shortening and combining prayers. This ruling also applies to a period of less than four days at the workplace. The fact that the questioner is continuously employed and has a private residence does not alter the ruling. As for the period the questioner spends with his wife at her residence, he is not permitted to shorten prayers during that time, because the mere arrival of a traveler to his wife severs the status of travel.