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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, it should be noted that it is not permissible for this girl to talk to you because you are a marriageable man to her. This is even more confirmed in her regard as her mother prohibited her from doing so, in addition to her making an oath by putting her hands on the (text Book of the) Quran.
Since she spoke to you, then she is obliged to expiate for breaking her oath; for more benefit, please refer to Fatwa 81501.
The fact that she was forced to make this oath has no effect as the harm she feared would have afflicted others and not her. Therefore, both of you are obliged to repent to Allaah and stop talking to each other.
If you still want to marry this girl, then you have to endeavour to convince her mother. If the matter is facilitated, then all perfect praise be to Allaah, otherwise you have to forget about marrying her. In addition to this, she is not permitted to go against her mother's will and marry you, as the scholars stated that any act which may greatly harm the parent is considered to be un-dutifulness towards parents, provided that such an act is not an obligation on the son.
Furthermore, it is known that if a girl marries someone from another country than hers, then this will harm her parents due to long absences and the like.
You undoubtedly know that there are other choices and the matter is easy; if a man can not marry a particular woman, it might be that Allaah will bless him with a better woman, and perhaps Allaah has repelled harm from him by not enabling him to marry that woman. Allaah Says (what means): {… and it may be that you dislike a thing which is good for you and that you like a thing which is bad for you. Allaah knows but you do not know.}[Quran 2:216].