My brother and I share the same PC, but we each have our own Steam accounts. Before Steam mobile authentication was introduced, we did the good old trick of adding the -login %u %p parameters to two different shortcuts of Steam, allowing each of us to switch accounts easily without re-entering passwords each time.
Now, with the mobile authentication, we have to enter a mobile code each time one of us logs in, regardless of whether or not we use two different shortcuts.
The only way to overcome this is by checking the "remember me" box, but this will only work if you've one account, because once you log out, it will ask for the code next time you log in.
Is there anyway to overcome this by making Steam remember the PC or something? It truly is stressful to be forced to have my mobile on me whenever I need to use Steam.
Best Answer
You say you both use the same Windows account.
Create a new account for your brother. Login to steam with his account information. Sign in back as your shared account. Create a new shortcut to steam and change the command to
(make sure to use the full path to Steam.exe from the original shortcut)
Now, when your brother wants to use his Steam account, all he has to do is close Steam, and run it again through this shortcut.
Do note that Steam will use the new windows profile, so if your brother has games that store configuration or saved games in the user profile, he will need to copy them over to the new account.