What is the ruling on the Dhuhr prayer if its time arrived while I was in a city an hour and a half away from my city, and I remained there until the time for the Asr prayer began, then returned to my city while the Asr prayer was still due upon me?

Shortening prayers (qasr) is a Sunnah (definition) for a traveler on a permissible journey exceeding 83 kilometers. Combining prayers (jam') is permissible. The decisive factor is the distance, not the time.

So, if your journey is permissible and the distance is not less than what was mentioned, then it is sunnah for you to shorten prayers. Combining prayers is permissible during the journey, just as it is permissible to avail oneself of travel concessions during the period of stay in the destination city, provided you do not intend a residence that would terminate the ruling of travel (four days or more according to the majority of scholars).

If you return to your place of residence before praying 'Asr after having prayed Dhuhr while traveling, you must complete it because the ruling of travel has ceased. A missed prayer from travel is made up in residence as a full prayer. It is not permissible for a woman to travel without a mahram (definition) except in specific cases.