Perry is spot-on as usual. You will need to pick a "master" sql instance and then script out the logins with the SID and then replace all existing instances with the new login (drop/create). Once that is done the database will be accessible by those logins because the SIDs are the same all around. Easy-peasy, lemon-squeezy ... once you know the trick!! 😎
Best,
Kevin G. Boles
SQL Server Consultant
SQL MVP 2007-2012
TheSQLGuru on googles mail service