The first wife’s approval is not a condition for marrying a second wife

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. Fatawa 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 Allah 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-Albani in Saheeh Sunan al-Nasaa’i, no. 3682). 

When Allah 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 Allah commands that a man should restrict himself to one wife, if he knows that he cannot be just. And Allah is the source of strength. 

See Fatawa Manaar al-Islam, 2/570.