All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is the nature of a woman to be jealous about her husband. This is a matter that all women feel whatever their level of piety and religion is. If any women could have been free from this, it would have been the mothers of the believers who were the wives of the Prophet . Indeed, it is reported in the Sunnah that they were jealous of each other. Imaam Muslim reported that the Prophet went out of his room by night when it was 'Aa'ishah's turn. So she followed him thinking that he was going to his other wives [but indeed he went to Al-Baqee' graveyard]. The Prophet discovered when he came back that she was following him and he asked her: "Were you jealous, O 'Aa'ishah [thinking that I had gone to another wife]? She replied: "How is it that a person like myself would not be jealous about a person like yourself?"
So there is no harm if jealousy is within reasonable bounds. However, it is not religiously acceptable that jealousy would reach the extent that a woman reaches the point of asking her husband to divorce her. It is not permissible for a woman to ask for divorce just because her husband marries a second wife, since he is only doing what Allaah has permitted him to do, and if he remarries, this does not cause any harm to his first wife unless he is not just between them. The Prophet said: "The smell of Paradise is forbidden for any woman who asks her husband to divorce her without a valid (Islamic) excuse." [Ahmad and Abu Daawood]
Therefore, a woman is obliged to accept what Allaah has legislated and be pleased with His Decree and Predestination. She should repel the whispers of the devil, stay with her husband and be pleased with what Allaah has predestined for her.
Allaah Knows best.