Is it permissible for him to go to his second wife if he forsakes his first
wife for a shar’i reason [i.e., withholds conjugal relations for
disciplinary purposes]? Or should he stay in the same house with the wife
whom he is forsaking?

Praise be to Allaah. 

We
put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may
Allaah preserve him, who answered as follows:

 For
the sake of dividing his time fairly among his wives, giving each wife a
night and a day, he should stay with her. And Allaah knows best.