Move DB/LOG files - Detach/Attach - Problem
The correct (and preferred) way in my opinion should be 


Use alter database....MODIFY FILE - This will update system catalog.
Offline the database
Physically move the files to the new location that you specified in step 1.
Online the database


I have written a script to rename a database - db name and the files -logical and physical and you can use that logic to adjust it as per your requirements.

Note: Before doing any detach/attach, you should take a full backup of the database. See Bad Habits: Using MDF/LDF Files .. from Aaron Bertrand.