ENTP.
I see that we agree on her Ti-Fe preference so I won't elaborate on that.
But I think her blatant stance on not having children and repressing everything that's conventional, including family, marriage, a "normal" life (as in responsible, role model) and advertising her drinking, one-night stands, and "special" relationship with her father (as in she hates him) is more than Ti's habit to dissect values and being "unorthodox".
So I think it's her inferior Si coupled with her dominant Ne is that rebels against conventionalities and trying to show a new way of life.
ENTPs often change the world and she has ideas that are definitely out of range for a Se dom.
She has remarks and a humor that is so unconventional and so original that it's hard for me to type her anything other than ENTP.
(hey it's a female ENTP. so that's what it looks like)