When my members are logging in it says Welcome and then brings them right back to the login screen. The only way to fix this is for them to delete all of their cookies. What could be the cause of this?
Instead of making your members delete their cookies, just change your cookie name in coppermine's config (make sure to use a valid cookie name). This will have the same result as if you deleted all local cookies of all your users. Next time they visit your gallery, they will all have to log in once more.
Impossible to tell you what is actually wrong without more information. You could have posted a link to your gallery and a non-admin test user account for a start.
Thank you for your help GauGau I never thought of that. :-\