She tried to 'put on a brave face' [=she tried to appear brave or calm] despite the pain of the injury.
You can refuse to talk to her if you like, but you're just 'cutting off your nose to spite your face'.
They made it on time 'in spite of the fact' that they got a flat tire.
(..) ...surrounding himself with total nincompoops? I'm back, Mr. Luthor. I was just talking about you. You were followed again. In spite of those cat-like reflexes. Mr. Luthor, l'm sorry. Is that the newspaper I asked you to get me? Yes. Then why am I not reading it? (..)1978 Superman