Name of a film about a family fleeing global warming related disaster in America

The film must have come out before 2012 and it was about a family in the southern USA. For some reason, they had to flee their home and they end up on a boat and travel through America, eventually ending up in Canada, I think. I do not remember much about it as I had rented it from a Library when I was a kid before 2012. It may be early 2000s or 1990s. I remember that it made a big deal of America being a third world country due to global warming and a lot of the film took place on the river-boat/raft.

Also, I'm looking for a different film about a man living in the woods after a post apocalyptic event, probably a disease. He wields two axes and is extremely good at fighting. He is being hunted by mohawk wearing, genetically engineered humans who may be clones and were owned by a corporation. They landed in a helicopter to capture the man because he had magic blood or something and he kills them with his axes. The genetically modified mohawk warriors used guns I think. The protagonist either doesn't speak at all or not much.