I don't understand the concept of storing encrypted stuff in a cookie when it is the encrypted version of it that you need to do your hacking. If I'm missing something, please comment.
I am thinking about taking this approach to 'Remember Me'. If you can see any issues, please comment.
Create a table to store "Remember Me" data in - separate to the user table so that I can log in from multiple devices.
On successful login (with Remember Me ticked):
a) Generate a unique random string to be used as the UserID on this machine: bigUserID
b) Generate a unique random string: bigKey
c) Store a cookie: bigUserID:bigKey
d) In the "Remember Me" table, add a record with: UserID, IP Address, bigUserID, bigKey
If trying to access something that requires login:
a) Check for the cookie and search for bigUserID & bigKey with a matching IP address
b) If you find it, Log the person in but set a flag in the user table "soft login" so that for any dangerous operations, you can prompt for a full login.
On logout, Mark all the "Remember Me" records for that user as expired.
The only vulnerabilities that I can see is;