Can a Woman Ask For Divorce?
Question

If a couple differs in their Islamic perceptions; one who grew up in the West and the other in the East, and they quarrel constantly and can't come to an agreement, at what point is talaq considered? Is it wrong for a sister to ask for talaq? Will she be punished on the Day of Judgment? Does the ‘Arsh of Ar-Rahman shake once talaq is asked for? This is what one sister, growing up in the West, is being told by her husband from the East.
Praise be to Allah.Divorce in Islam
The divorce of a Muslim woman from her husband is an affair which is loathsome to Allah and not a praiseworthy event. This is due to the problems and possible evils. 
When can a woman ask for divorce?
However, if there is a situation in the marital life taking place between the man and the woman, due to a defect or defects in one or both of them, such as problems of Din, bad character, sickness, or a defect such as being sterile or similar, then out of the mercy of Allah, seeking divorce is permissible. In this case, it is okay and there is nothing prohibited in seeking a divorce .
Seeking divorce for no reason
The thing which is prohibited is a wife seeking a divorce from her husband for no (valid) reason in the Shari’ah. There is a serious promise made for seeking a divorce without a valid reason. It is reported in the hadith of the Prophet (peace and blessings of Allah be upon him), "If a woman asks her husband for a divorce, for no reason, then the smell of Paradise is forbidden for her". (At-Tirmidhi narrated it. He said this is a hasan hadith. Sunan At-Tirmidhi, 1187.)
Does the Throne of Allah shake because of divorce?
The hadith "Marry and do not divorce for verily divorce causes the ‘Arsh (Throne of Allah) to shake " is forged and da'if. (Al-Jami` al-Saghir, 2429)
And Allah knows best.