Is a man married to two women permitted to spend every night with his second wife during her short stay with him, while visiting his first wife and children during the day, or must he be fair in spending nights between the two wives?

The second wife has the right to equitable division of nights. Her presence in another country does not negate her right to division, unless she is disobedient (nashiz). The husband must make up the time he spent with the first wife, unless the second wife relinquishes her right. If it is the second wife's turn, then it is not permissible to enter upon the first wife except out of necessity.