the remember me and auto login options are controlled by cookies, you will need to edit the set cookie values behaviors on the admin login to change the names of the cookies that get created, then edit the second authenticate user behavior to change the login to use the new cookie names.
Setting it up this way, using 2 separate tables and separate login pages is not necessary though. I don't recommend this set up.
It would be better to use one table and use User Level Authentication.
Add a column to the table for user level, set the default value for that column to 1. Then edit the Authenticate user behavior to store the user level in a session.
Use the user level session in access rules to create a Basic User level rule:
User Level Session is = to 1
and an admin rule:
User Level Session is = to 2
for users that should be admins, edit the databases to set the user level column to 2