What is the ruling on a man traveling with one of his wives without the consent of the other, and if he travels, does he have to make up for the other? And how does he justly divide his time between his wives in terms of overnight stays and sitting with one of them to care for her children?

A polygamous husband must be just among his wives in what Allah has obligated him to be just. If he wishes to travel with one of them, the prevalent opinion is that this should be determined by lot (drawing lots). If he travels with one of them after drawing lots, he is not obliged to make up the nights for the remaining wives upon his return. However, if he travels with her without drawing lots, he must make up those nights. If the wife travels with her consent, she has no right to demand that the nights be made up. Justice in staying overnight requires him to stay with each wife for her entire night, and he should not enter upon her co-wife except for a need or necessity, or with the permission of the wife whose night it is. The day is considered a تابع (extension) of the night of the wife with whom he stays.