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.
It is permissible for the husband to stay with his other wife on the day allocated for her co-wife as long as the latter is not in her house on her turn for a reason that she is responsible for, such as being at work. This is because the husband could not fulfill her rights over him by spending that time with her because of a reason on her part; thus, her right to that time is waived.
Ibn Qudaamah wrote, "In brief, if the wife traveled for a need with the permission of her husband to pursue trade, or for a visit, or to perform Hajj or ʻUmrah, then her right to financial maintenance and her turn (of spending the night) is waived during this time. This opinion was adopted by Al-Khiraqi and Al-Qaadhi." [Al-Mughni]
He also added, "This is because allocating her a turn (of spending the night) is for the purpose of intimacy, and the maintenance is to allow the husband to exercise his right of sexual enjoyment with his wife, and this was hindered because of a reason on the wife’s part; her right to this is waived accordingly..." [Al-Mughni]
Allaah knows best.