Question Summary:
Can a woman take khula because her husband wants to marry another woman?

Question Detail:

Can a Muslim Women take khula based on her husband's second marriage to another women. Is this allowed in Islam as she does not want to get divorce for the sake of children

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
If a wife does not want to remain in the marriage due to being oppressed, the wife may request the husband to accept khula if he refuses to divorce her. Khula is where a wife requests a divorce from her husband in exchange of returning her mehar (dowry).[1]
If the husband accepts the proposal of khula, then that will constitute a talaq-e-ba’in (an irrevocable divorce). If he does not accept the khula proposal, then the marriage will remain intact.
It is clear from above that the end result of khula and talaq (divorce) is the same.
If a woman does not want a divorce, then she should not even seek khula as that will also end up in a divorce. In any event divorce is abhorred in Islam. And every possible avenue should be exhausted to address the imbalances in a marriage to save the marriage.
  
And Allah Ta’āla Knows Best
Ismail Dawoodjee                 
Student Darul Iftaa
Zambia
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net