Via a desktop shortcut, an admin will launch a shell as another user. The user should go into the shell with no elevated privileges, but execute the first command with elevated privileges. In the end, the user should be in non-privileged shell that is kept open for further use.
How do I do this?
Question Edited For WIP Answer.
gksudo "gnome-terminal --execute bash -c 'boss "apt-get update"; bash'"
Does not work.
What follows is the answer thanks to Laurent helping me brainstorm. Unfortunately my situation was too sophisticated for me to express well.
I have an admin user who never goes online. He uses proxy users to fetch things and do his bidding. The user named update is in the sudoers file and is allowed to apt-get with NOPASSWD. admin wants a shortcut leading to a gnome-terminal that automatically calls apt-get update upon execution because admin wants to install something right after that, something that can't be predicted to be put in a script. Auto updates won't work for admin, because admin is fire-walled from the internet and is forced to hire goons for system updates and fetching other downloads.
Thank you Laurent for leading me to the right answer! Here it is:
gksudo -u update "gnome-terminal --execute bash -c 'sudo apt-get update;bash'"