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.
(..) Don't forget, Howard, we're not using the . The first attempt on President Ford's life was days ago... and again yesterday in San Francisco. ln spite of the two attempts, Mr. Ford says... he will not become a prisoner of the Oval Office... a hostage of would-be assassins. (..)1976 Network