I'm having trouble with a custom login/lost password form on a site I'm building. The site is completely password protected. I have a custom login page and I'm using 'wp_login_failed' and 'authenticate' hooks to manage/redirect failed attempts and empty field when logging in. These work fine and the user stays on my custom login page and gets error messages when they have a failed login attempt.
How would I change this to go to my custom login page instead?