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 happened to saluting an officer when he leaves the room? Open it up. I don't believe it. Dawson's gonna go to jail just to spite me. Fine. If he wants to jump off a cliff, that's his business. I'm not gonna hold his hand on the way. I want to get him a new lawyer. How? (..)1992 A Few Good Men