It was just a fluke that they found the entrance to the chute anyways - if they'd been sane instead of going for that crazy mine cart ride and hadn't let the cart blast through that wall they would have been stuffed and the movie would have likely been a tragedy!
Well according to the book, granted this was intended to come afterward, they do choose the wrong cave... and its a dead end. They are forced to backtrack when food and water become scarce. since they were looking through the book in the movie its easy to assume they knew which way to go.
unfortunately neither movie really follows the book too closely... in spirit the original held very close to the original, the remake had a few glimpses we missed in the original, but altering the storyline just makes the story a bit light and unsatisfying... the book is hardly without flaws, but it could have been handled better in its adaptations.