What is the ruling on a fasting person breaking their fast in Ramadan after their journey has ended, and not during it, especially since they have two homes in the areas of travel, and what is the expiation for this breaking of fast if it is not permissible?

If you are a traveler who has broken your fast and your journey ends during the day, and you continue to break your fast without abstaining, scholars have differed regarding the ruling on this. Some believe that what you did is permissible because breaking the fast was for a legitimate reason (travel), and you must make up that day. Others believe that you must abstain because the concession for travel has ended.

The preponderant opinion is that you are not required to abstain for the rest of the day. Ibn Uthaymeen, may Allah have mercy on him, was asked about a traveler who arrives in his hometown while having broken his fast. He replied that he is not required to abstain and may eat and drink for the rest of his day, because his abstaining would not benefit him in any way since he is obliged to make up that day anyway. This is the correct opinion, and it is the madhhab of Malik and Shafi'i, and one of the two narrations from Imam Ahmad, may Allah have mercy on him. However, he should not eat and drink openly.