I'm married with two kids and my husband cheated on me and took her in marriage as a second wife. I don't feel loved anymore.
Can I ask for a talaq?
Surely it's permissible for the wife to ask her husband to give her talaq (which is halal, although disliked). If the husband agrees, he can make it happen:
In classical Islamic law it refers to the husband's right to dissolve the marriage by simply announcing to his wife that he repudiates her. It requires neither justification nor court approval.
Although the husband may refuse to give her talaq. In this case, an option for the wife is requesting khula, not because of the husband's second marriage, but because of the wife's inability to satisfy her marriage commitment:
But if it so happens that a woman cannot put up with that and the fears that she will not be able to fulfil her husband’s rights over her if he takes a second wife, then she may request khula‘ and return the mahr to the husband ... -- Islam Q&A
Khula ordinarily requires (a) court approval, and (b) returning the mahr. From what I understand, the exact procedure varies from place to place.
Assalamu alaikum sister
I can understand your feeling in this situation. No women, either Muslim or non-Muslim, wishes to share her husband with anyone else. But still, if you really wish to follow the commandments of Allah, please maintain patience. Don't go for khula, because Allah hates Khula or Talaq.
Allah allows men to have four wives but only one condition that is to treat each wives equally if not fear Allah.
And if you fear that you will not deal justly with the orphan girls, then marry those that please you of [other] women, two or three or four. But if you fear that you will not be just, then [marry only] one or those your right hand possesses. That is more suitable that you may not incline [to injustice]. Quran 4:3
This is powerful ayat. If a man thinks he can have upto four wives and treat them unequally, then he will be put into trouble on the Day of Judgement. Allah knows that men can't be just, that's why Allah asks men to have one.
For example, If a husband bought a gold chain for the second wife then he has to get the same gold chain (as the same amount worth of that) to the first wife. His burden is doubled for what he had made. As for you, it is different. You have only one spouse to fulfil his need.
So comparing you both in Allah's questions regarding marriage life on the Day of Judgement, questions asked to you will be lesser than questions asked to your husband. Be patient if you cant, make dua to Allah for patience.