Is the husband obligated to compensate his wife for the nights she missed from staying overnight with him due to her traveling to her family's house with his permission, knowing that it was her night upon his return, but he will stay with his other wife for days before coming to pick her up?

If the husband returns from a journey and begins with his other wife, staying with her for days, he must make up those days to you, unless you willingly forgo your right. Al-Hajawi said: "And if he sends her away for his need, or she moves from one city to another with his permission, her right to maintenance and division is not forfeited. He must make it up to her according to the time he spent with her co-wife."