All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is not obligatory on this man to stay in your sister's house since he has divorced her, and he does not have to spend the night equally between his other wife and her. He is allowed to come home whenever he wants to visit his children, if any, or for any other permissible reason.
If this is a revocable divorce, then she is like his wife, it is permissible for him to stay alone with her, and it is allowed for her to beautify herself to him so that he may take her back as a wife. This is the opinion of some jurists. However, if this is an irrevocable divorce, then he is not allowed to enter to her home or stay in seclusion with her except with a Mahram.
Lastly, it should be noted that one has to endeavour to take this wife back to her husband if it is a revocable divorce, but if the waiting period has expired he can only take her back with a new marriage contract.
Allaah knows best.