Whats with the caps?

I would need a reason to drive to the other side of the planet, why would my mother and I leave the planet?

You Live In A World Only Desert. Everyone But You And Your Mother Are Alive.

No. That can't work, because everyone else except you and your mom is alive, so that means your protagonists are dead. Spanky, your question is unclear, to say the least. When you ask if the "game" could work (in quotes because it sounds more like a story than a game), what is it you are trying to find out?
It's technically feasible, if that's what you're asking - all it needs is a design, a team, and a business plan. Or are you asking if it could be marketed (if it might sell)? Or are you asking if the story is compelling?
I recommend you read How To Ask Good Questions and try again.