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.
(..) what happens to Laszlo? I'm not. But I am interested in what happens to llsa and me. We have a legal right to go, but people have been held here... ...in spite of their legal rights. Why do you think we want to hold you? Ilsa is Laszlo's wife. She probably knows things Strasser would like to know. (..)1942 Casablanca