Cannot access directory through standard user even when permission is given
I solved the problem.

When I ran:

chmod -R 777 /vpn/directory


What I actually ran was:

chmod -R 747 /vpn/directory


So, the group wheel had only read permission. I thought my standard account was not part of the group wheel and I ran 

dscacheutil -q group | grep 'wheel' -A 4 


To make sure. I got the output:

name: wheel
password: *
gid: 0
users: root 

--
name: wheel
password: *
gid: 0
users: root 


However, after running:

chmod -R 777 /vpn/directory


I am now able to access the files I need.

Thank you very much.