How are the extended privleges set.. especially fmapp
"people can no longer login remotely without opening the file using the option key"
That sounds like you've set a default account name and password in File Options.
"Somehow the old password is saved somewhere on each computer. "
Have you set up account names and user names to be the same?
A user name is set in preferences. When you open a password protected Filemaker file, Filemaker automatically enters this User name in the Account name box of the password log in and this can be confusing in some cases.