Praise be to Allah.
If the situation is as described, and he has taken both houses as his place of residence, then it is not permissible for him to avail himself of the concession of travelling with regard to shortening prayers and other things when he is staying in either of the two cities, but he may avail himself of the concessions whilst travelling between the two cities, if the distance between the two cities is that which allows shortening of prayers, which is approximately 80 km.
And Allaah is the source of strength. May Allaah sent blessings upon our Prophet Muhammad and his family and Companions. End quote
Standing Committee For Academic Research and Issuing Fatwas