Is he sinning if he keeps one of his wives with him and sends the other back to his homeland?
The husband must treat co-wives fairly with regard to staying overnight with them, spending and providing accommodation. This fairness is a condition of plural marriage being permissible. Allaah says (interpretation of the meaning):
“marry (other) women of your choice, two or three, or four; but if you fear that you shall not be able to deal justly (with them), then only one”
Abu Dawood (2133) narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever has two wives and inclines more towards one of them will come on the Day of Resurrection with half of his body leaning.” Classed as saheeh by al-Albaani in Irwa’ al-Ghaleel (2017).
The husband has no right to show preference to one of his wives by keeping her with him and sending the other one back to her family. Rather he must treat them fairly and keep one of them for a while and send the other one away, then reverse the situation, and so on, so that each of them will have the rights that Allaah has prescribed for her.
If one of the two wives agrees to give up her rights and does not mind if the other wife is favoured over her, there is nothing wrong with that, but that is subject to the condition that it be with her consent, without any force or compulsion from the husband, and whenever the man is able to treat both wives fairly, that is what he must do.
We put your question to Shaykh Dr. Khaalid al-Mushayqih (may Allaah preserve him) and he said: Yes, he must treat his wives fairly, because Allaah says (interpretation of the meaning): “and live with them honourably” [al-Nisa’ 4:19]. Living with them honourably does not include keeping one and sending the other away, rather he must treat them fairly, either by keeping one for a while then sending her away and bringing the other, and so on, or by coming to some agreement with the one whom he sent away that he will come and visit her in her homeland or will give her some money or work out some other agreement and so on. End quote.
And Allaah knows best.