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 repented to Allaah and became pleasing in her religion and moral conduct, then you should continue to attempt to convince your mother. First, you should supplicate Allaah about this and then seek the help of whomever you think may influence her. Then, if she agrees to your marriage to that girl, praise be to Allaah, but if she insists on refusing her, then in principle you should obey her and it is not permissible for you to marry that girl while your mother objects; for more benefit, please refer to Fatwa 83379.
However, if you fear to be afflicted by that girl and do with her what displeases Allaah because of loving her, then in this case you are permitted to marry her even without the consent of your mother; in which case, you should endeavour to please her. For more benefit, please refer to Fatwa 116872.
On the other hand, it should be noted that the fact that that girl had sinned in the past is not an impediment from marrying her if she had repented to Allaah.
In any case, we advise you first to perform the Istikhaarah prayer and supplicate Allaah to choose what is good for you, because a person does not know what is good for him; for more benefit, please refer to Fatwa 81434.
Finally, you should hold fast to the Orders of Allaah in all your matters and affairs and be reasonable and rational.
Allaah Knows best.