Is it permissible for a husband to bring his second wife to work in Saudi Arabia, while he is unable to bring his first wife and children, and is this considered just among wives?

A husband must be just among his wives. The Shafi'is and Hanbalis agree that a husband is not permitted to travel with some of his wives unless they consent or through drawing lots, basing their view on the hadith of Aisha (may Allah be pleased with her) that when the Prophet (peace be upon him) intended to travel, he would draw lots among his wives. As for the Hanafis and Malikis, they held that a husband may travel with whomever he wishes without drawing lots or seeking the consent of the other wives, but they elaborated on this. The drawing of lots is to be between the wives who are suitable for travel. If one of the wives is unable to travel, it is permissible to travel with another without drawing lots, provided the wife who did not travel is appeased. If the travel is for the benefit of one of the wives and not as a preference for her, there is no harm in it, provided the other wife is appeased.