What should this wife do, what are her rights, and how can she preserve them, in light of her husband abandoning her after promising her justice, and his infrequent overnight stays with her, all while he makes excuses about his children and circumstances?

A husband must be just among his wives, and preferring one over another in matters where justice is obligatory is a major sin. A potential worldly punishment has been reported for the oppressor, and a punishment in the afterlife for one who deviates from justice, which is that he will come on the Day of Resurrection with one side of his body drooping or fallen. It is not permissible for a husband to enter upon one wife during the turn of another, except out of necessity. It is forbidden for him to abandon his wife without a legitimate religious reason, and this is one of the justifications for seeking divorce. The wife must remind her husband to be just, and if he does not respond, she has the right to take the matter to the Sharia court.