What should a wife do who lives alone in her apartment abroad, and whose husband's family demands the keys to her rooms, refusing to accept that they are not given to them, knowing that they have the apartment key and that she does not wish to give them the keys due to previous problems with them?

A woman is not obliged to give the keys to her apartment rooms to anyone, especially if they are non-mahram (definition), such as the husband's brothers. It is forbidden for her to receive them alone in her apartment or to hand them the keys for them to enter and exit as they please. If they request the keys while she is traveling, they have no right to them unless there is a genuine interest, in which case she should discuss it with her husband so that he can deal with his family.