If she was too tired to really put all of her strength into pulling the cart, it's possible. I mainly remember the cart tipping over when she tried pulling it up a hill. She was too weak from exhaustion to pull it, and when she stopped, gravity got the better of the cart, and there was the weight imbalance.
Of course, this is a cartoon, and cartoon physics tend to defy real physics.
Yeah, you're right about her head. It was a problem I noticed early on, but couldn't really do anything about due to the time limit. The problem is her neck is covered up and sorta looks like it expands her head because it's at a flat angle. In the show, the animators avoid this by curving the pony's backs when they lie down, or by showing them laying from a top view.