Assalamualaikum.
I think you are talking about Pakistani Islamic marriage law.
Islamic marriage (and divorce) law in all Muslim countries are based on Qur'an and sunah, but not really same between one country and other countries.
I give an example, This is the the translation of "sighat ta'lik" (addendum about wife's right to get divorce) in Indonesia that be spoken by the husband in nikah procession.
---------------
After marriage agreement, I am .......................................... son of Mr. ..............................................
I here with promise thruthfully that I will fulfill my obligation as a husband,
and I will associate my wife named ...................................................
daughter of Mr. ..................................................... kindly ( mu’asyarah bil ma’rufi ) according to the teaching of Islamic religion.
Furthermore, I read this sighat taklik for my wife mentioned as
follows :
Any time :
1. I leave my wife two years continuously ;
2. Or I do not give compulsory basic necessities of life three months long ;
3. Or I hurt my wife’s body / physic ;
4. Or I neglect / I do not care my wife for six months long.
Then my wife is not willing and my wife complains about her matter to the Religious Court and her complains is accepted by the court, and my wife pays money in the amount of Rp. 10.000,- ( ten thousand rupiahs) as 'iwadh ( substitute) to me, then falls my once divorce to her.
To the court mentioned I authorize to receive the substitute money and then to hand over it for the need of social devotion.
(city/location), ..................................
Husband
----------------
(ten thousand rupiah is equal as 1.1 US$)
Source:
http://kuapasarminggu.blogspot.com/2009/07/sighat-talik-bahasa-inggris.html
Mahr is not mentioned in that Indonesian "sighat ta'lik", and never became a reason to get divorced because in Indonesian culture, mahr usualy not in form of money, but in form of Qur'an, sajadah (prayer mat), and mukena (woman's salah clothe). Money is additional mahr that not mandatory.
And, do Muslim women have a right to ask divorce, or get divorce?.
From what I know, ulama are not in single opinion about it. There are ulama who allow women to ask divorce, there are ulama who forbid women to ask divorce. Ulama in Indonesia allow women to ask divorce with acceptable reason. Indonesian Muslim women can go to KUA (sharia affair office) if they want to get divorce. But from what I've read, ulama in Saudi Arabia issued a fatawa which mentions, women should not ask divorce.