How can I remove laminate flooring from an oddly shaped hallway without destroying it?
The rule of thumb is, "last pieces down are the first and easiest to remove".
If the hallway was the last to be laid, it will be an easy pull. That would be the first that needs to pull up. Remove the shoe mold, remove the damaged flooring, you may need to remove some that is not damaged to easily remove it all. Once you see how the first few pieces come up the rest will be easy. It will only be easy to remove in a given direction only. If the room to the right was done last then the removal will need to start with a saw cut at the opening. The replacement may take a glued joint or transition strip to change the direction of the "lay" of the floor.