When in doubt, rely on the aid of kindly elderly people. Kevin basically does that when Marley saves him, and his mother does it earlier in the movie.
While the rest of the McCallister family is willing to wait until Friday to fly back the U.S., Kate (Kevin's mom) is determined to get back to her son as soon as possible, despite the lack of available flights. She convinces a pair of married American travelers to give her their seats on a flight, offering them two first class tickets, her watch, a ring, five hundred bucks, her earrings, and a pocket translator.
The traveler husband's eager to quash his wife's sympathies, but Kate is persistent:
KATE: I'm desperate. I'm begging you, from a mother to a mother—please!
This tugs at the old lady's maternal heartstrings, and they give in. Thanks to these malleable travelers, Kate's able to get back to the U.S.—although she could've taken the Friday flight and ended up getting back at the same time, given how long it ends up taking her.