Turning iMessage off doesn't work, or what you tried?
Either way, a separate Apple ID is best anyway, a separate ID will solve it. Just remember the one that gets a new ID will not be able to update any apps that were downloaded/purchased on the other ID. They can continue to use the apps but they will keep getting the message that the ID/password is wrong to update the apps.
To get rid of the nag they will have delete the apps and d/l or purchase them using the new ID. They will lose settings and data. You can't transfer an app to another user.
It's easier at first to just use the same ID, but doesn't work out in the long run,