How do I replace insulation in the corner?
I wouldn't attempt to remove the existing insulation unless there's a health hazard (e.g. mold). It was put there during the middle of framing because of how difficult the space is to access. My personal solution would be to spray a little big gap filler in there because it's designed to expand and provide an airtight seal. Other types of insulation, like fiberglass and Roxul lose their effectiveness when compressed. Much of the insulation in them comes from trapping air in pockets. So you'd get less efficiency after cramming it through a small crack.