Forgot the password of a keychain (non the login one)

First, setting up separate admin and standard accounts was NOT a mistake. It is, in fact, a Good Idea™.

When you need to authenticate (for example, to unlock a padlock), you need to enter both your admin name and your admin password. If you're in your admin account, the name will be filled in for you. If you're in your standard account, both the name and password fields will be blank, and you need to enter them both. Be sure to enter the admin's name and the admin's password.

The login (user account) password isn't stored in keychain access, but keychain access automatically adopts the user account password as the keychain access password by default.

So, your password for keychain access is most likely the same as the login password.

There is no default password in mac, the user creates one on install. If your mac was provided already installed, there was likely an assigned password created by the admin, perhaps associated with AD. If you reinstalled OSX, it would not have wiped the password, but if you formatted the harddrive, then reinstalled OSX, you would have created a new password.