Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Shortening the prayer of 4 (Rak’ah) units (Zuhr, Asr and Isha) is permissible for every traveler who is travelling a distance of 83 Km. The traveler does not perform a full prayer except if he goes back to his place of residence from where he started his journey or to the place where he still lives, or a place where he gets married with a wife, or when he intends to stay for four days in a place without leaving it.
If the wife is travelling with her husband she has to shorten the prayer when her husband does so. When it becomes permissible for the husband to shorten the prayer while she is travelling with him, it is permissible for her to shorten the prayer as well.
Therefore, your sister has to shorten the prayer during all her travel if the distance between the two towns is a distance of Qasr (a distance that permits shortening the prayer).
As for the period she spends in those towns mentioned (in your question), she should not shorten the prayer unless the period is less than 4 days excluding the day of arrival and the day of departure.
The fact that her husband owns a house in Karachi, or that his wife is from Hyderabad, or that the family or his wife are from Multan, all of these facts do not prevent her from shortening the prayers, as long as there is no other reason that prevent shortening the prayer as mentioned above.