The sudo command is only really intended to enable a user to run a specific command as the superuser or another user.
The correct method is to create a group which the root user and your 'other' user both belong to, then create the directory, and ensure that whenever either root or the user needs to read/write to that directory, they have changed their effective group.
There is a possible method that involves allowing a user to execute a shell call, such as bash or csh etc, but I would strongly advise against this. If you do investigate this area, you still need to use a specific group to lock down the directory and scope.
Not a good approach
C