No sarcasm intended. Just facts. I'm surprised it wouldn't accept your admin password, that's what it is asking for. You might have a read of this article to see if there is anything there to give you something to try.
Ok, thanks for the added info.... looked at your link, so the Key Chain thing is to do with email as your link says ? If it is, I don't have any problem with the Key Chain box constantly popping up on my account, it's on my teenage daughters account and she doesn't even use email. The popping up every second has stopped her from using the account, she now uses mine. I made a guest user account and it also does it on there!
Well, if it's her account that is causing the popup, and if she doesn't use it, just open her account and provide Keychain an admin password. I had thought from your original post that it was popping up in YOUR account for the Keychain password. When you open Keychain, you have to give an Administrators password. Assuming your account is an Admin account, your password should do. Once you've given it that first time, you shouldn't have to repeat it again. That's how it's working on my MBP. You'll need to repeat that on her login account on the MBP, if that's where the popups are occurring. What you are then saying to the OS is that "I am authorized to use Keychain" when you login to keychain from your account and "She is authorized to use keychain" when you repeat that on her account.