I login using an Admin account and then go to a restricted page. I then logout and go to the home page and try to login using a normal (non Admin) account. The website takes me to the restricted page and doesn't let me login and wants to 'make me' login to the restricted page.
Silverstripe probably stores the "last-visited" page (to redirect users to the correct protected page after the login procedure) somewhere, and it thinks you want to go to the protected page instead of the /admin.
You can call /admin after being logged in , right?