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My maternal grandfather (grandfather) married two women and my mother was from the second wife and I have an aunt who is from the first wife of my grandfather. Now I am in love with a girl who is the daughter of my aunt's daughter. By relation she is my niece.
So is it permissible in Islam to marry that girl?
Note: She is not my own sister's daughter but the daughter of my cousin's sister.
If I understand correctly, you're incorrectly considering her to be your niece. She is the daughter of your cousin's sister (cousin too, I suppose). So neither your cousin, your cousin's sister nor your cousin's sister's daughter is your mahram.
Therefore you can marry the girl.
To answer the question in title. No, one can't marry their nieces or nephews (niblings).
