What is the ruling of Islamic law on a man who divorced his first wife, with whom he has children, then married her sister for less than a month and divorced her, then returned and married his first wife again?

It is forbidden to combine two sisters [in marriage]. If the husband divorces one of the sisters, he is permitted to marry the other.

So, if a man divorces his first wife with an irrevocable divorce (such as khul’ or a triple divorce), or if her waiting period from a revocable divorce ends, he is permitted to marry her sister. This is forbidden if the first wife is still in her waiting period.

Similarly, he is permitted to return to his first wife with a new contract if he has not divorced her three times, provided that he divorces her second sister with khul’ or a triple divorce, or if her waiting period from a revocable divorce ends.

Whoever marries one of the sisters before the other one's marriage is definitively concluded has erred and must repent and stop cohabiting with the sister he wishes to continue with until he divorces the other.