In my terminal I run a screen. Obviously I have several tabs and in one of them I connect to a remote server. In this one I have a detached running screen, I attach it but I can't switch its tabs.
PS: the remote running screen has been here since many months ago and is never killed. However the local one is killed every night (company policy)
Either use a different command character for the inner screen, for instance by starting it with:
screen -e'^Bb'
So that ^B be the command character instead of ^A and a literal ^B be entered ^Bb.
Or you'll need to enter ^Aa (assuming the outer screen was started with the default settings, that is as if with screen -e'^Aa') for the outer screen to pass that ^A to the inner screen.
That also means that to enter a literal ^A in the inner screen, you'd need to enter ^Aa^Aa.
From within screen, you can change the default command character with the escape command. So for your inner screen already started in an outer screen both using ^A as their command character, you'd enter ^Aa:escape ^Bb to change the command character to ^B
