The first wife’s approval is not a condition for marrying a second wife
If a woman is married to a man and that this man is also married to an other woman without her, the last, knows about this marriage.
No need to say that this is a difficult and very exceptional situation but seems the best concerning the circumstances?
Praise be to Allaah.
The wife’s approval is not a condition for plural marriage, and it is not obligatory for the husband to have the approval of his first wife if he wants to marry a second wife. But it is good manners and kind treatment to approach the issue in such a way as to reduce the pain which women naturally feel in such cases, by smiling at her, greeting her warmly, speaking nicely to her and spending money on her according to his means, in order to gain her approval. Fataawa Islamiyyah, 3/204.
If a husband takes a second wife, he has to treat his wives equally as far as possible. If he does not treat them equally then he is exposing himself to a stern warning, for it was narrated from Abu Hurayrah that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever has two wives and inclines more towards one of them than the other, will come on the Day of Resurrection with half of his body leaning.” (narrated by al-Nisaa’i, ‘Ushrat al-Nisaa’, 3881; classed as saheeh by al-Albaani in Saheeh Sunan al-Nasaa’i, no. 3682).
When Allaah permitted us to marry more than one woman, He said (interpretation of the meaning):
“but if you fear that you shall not be able to deal justly (with them), then only one or (slaves) that your right hands possess. That is nearer to prevent you from doing injustice”[al-Nisaa’ 4:3]
So Allaah commands that a man should restrict himself to one wife, if he knows that he cannot be just. And Allaah is the source of strength.
See Fataawa Manaar al-Islam, 2/570.