All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
If this girl is righteous, then it is good to try again to convince her mother to agree to your marriage to her daughter. Harmony supports the continuity of good relations in marital life. And be keen on supplicating Allaah as much as possible as Allaah promised to answer the supplication of the one who supplicates him. Allaah says (what means): {And when My servants ask you [O Muhammad] concerning Me - indeed I am near. I respond to the invocation of the supplicant when he calls upon Me. So let them respond to Me [by obedience] and believe in Me that they may be [rightly] guided.} [Quran 2:186]
You may seek the help of some of her close friends or relatives whom you think she would respond to. Then, if she agrees, praise be to Allaah, otherwise you should leave this girl and look for another suitable wife.
On the other hand, the girl may try to persuade her mother, and if she is not convinced while she has no sound reason to refuse, then she has no right to prevent her daughter from accepting a competent and suitable man as a husband. The Islamic sharee'ah encourages accepting the proposal of the suitable suitor, as in the hadeeth narrated by Abu Hurayrah in which the Prophet said, "If a man whose religion and moral conduct are pleasing to you proposes to you, then let him marry." [At-Tirmithi and Ibn Maajah]
If the girl decides to be obedient to her mother, then Allaah may bless her with another husband with whom she would live happily in her religion and her worldly life. You must cut all relations with this girl as she is a non-mahram woman (marriageable/alien) to you and, perhaps, if you fear Allaah, then Allaah would bless you with a better wife, who will be a comfort to your eyes both in this life and in the Hereafter. Allaah says (what means): {And whoever fears Allaah - He will make for him a way out. And will provide for him from where he does not expect.} [Quran 65:2-3]
Finally, we point out that the mother has no authority in marrying off her daughter; it is only the girl’s paternal male relatives who can marry her off, and women have no eligibility in this. The men who are worthier in giving a woman in marriage are (in order): her father, her grandfather, her son, her full-brother, her half-brother from the father’s side, then their sons, then their grandsons, then her paternal uncles.
For more benefit, please refer to fatwa 83338.
Allaah knows best.