Does triple divorce occur if the husband said to his wife: "I divorce you by three if you step out of this door," then she left the apartment door, but did not go to her family's home, and the husband's intention was for the divorce to occur only if she went to her family's home, and not merely by stepping out of the door?

What is considered in oaths is the intention. So, if the swearer intends with his oath something that the wording can bear, his oath turns towards it. If the husband intended by his oath to prevent his wife from going to her family's house, and not merely exiting the door, then it appears that he has not broken his oath by her exiting the door. And the husband's statement is relied upon regarding his intention and purpose, because he knows his intention best. With the reminder that the permissible oath is swearing by Allah Almighty, and swearing by divorce is among the oaths of the dissolute, and it can lead to grave consequences.