In the beginning of the Temple of Doom, why wouldn't Willie just stay at the airport with Earl Weber? Maybe even go back to work for Lau Che?
She didn't steal the diamond, and Indy basically kidnapped her out of Club Obi Wan. Lau Che didn't seem to care if Indy hurt Willie (saying "You keep the girl, I find another") and was shooting at their car, but also wouldn't seem to care if she went back to work either. Even Weber recognized her as "Willie Scott the famous American female vocalist," so she should be safe with Weber, and rushing out of town didn't seem necessary.
Did Willie have any reason to leave Shanghai, with just the clothes she was wearing, and stay with the guy who "put two holes in her dress from Paris" and who's gun "burnt her fingers and cracked a nail?"