If there are no cars available near you, and you want to drive, try U-Haul or similar truck rental places. It’s probably not going to be a super comfortable ride, but you might get home.
That's a good idea, but not really feasible for a family. After the rental car fell through, we resigned ourselves to not getting to our destination and decided to make the most of the situation we have (explore a new city we have never experienced beyond an airport or a highway) and solidified our return flight.
A cheap mattress, pile of blankets, and a 12v tv all in the back of a truck made for the best road trips as a kid.
Sounds nostalgic and all, but the temp was near 0 in many places throughout the US. Not a fun time to be sleeping in the back of a U-Haul truck.
Or keep an eye out for shower-curtain-ring salesmen.
Or a polka band
the other 3 (expensive) hacks I can think of are charter a flight, and draft people stuck in the same situation to help defray costs, rent a 15-passenger van or bus to do it; buy any vehicle you can find and then resell it at the other end