Why does Dolly refuse to allow Marguerite to go to Sunday Island to get help? Why does their signal of a white sheet fail to gain notice?

Dolly refuses to allow Marguerite to go to Sunday Island for help after Joel's injury in Part 4 because she has no man to escort her. During the night, a deep fog comes over the area; therefore, the people of Sunday Island are unable to see the white sheet that is meant to signal trouble on Sargent's Point.