The answer depends a little on where do you live. As cats with such a pattern are for example an natural breed in some parts of the world, for example the grecian Egeian cat.
But in USA or other parts of Europe, I would say - I think she is a domestic, a red and white bi-color. I think also, with so much color, you can say she is a red tuxedo.
I set some words in bold. I do like you accept she isnt very cuddable nor loving. Its good. This way you KNOW when she cuddles and loves, she is voluntarily choosing to do so, to show you her friendship. Not because she is forced to, or it its expected from her, but because she wants to give her friendship and trust.
I promise you, she wil be more and more cuddly with the years, and as your friendship deepens.