Your diagram is very misdirecting.
The first moon is clearly attached, at the equator and its visible 'FACE' relentlessly FIXED to our (imaginary) Axial-pole and although rotating around the Earth, Not in and of itself.
Again - Try it yourself with a ball on a string/rod.
I have a ball on a stick, and can rotate it around me and the face is ever the same because it CANNOT rotate in its own right.... or my stick would be severed from it.
The moon's axis is not the same as the Earth's axis, It is an independant object and Does NOT rotate on its axis, but revolves around Earth's.
The Earth does ROTATE THOUGH, as a moon, around the sun and NEVER is one 'FACE' of it locked on the sun, and CANNOT BECAUSE WE ROTATE ON OUR OWN AXIS- If we didn't, then it would.
If the Earth stopped spinning at midday in London - it would always be midday in London - BECAUSE London-midday is now facially-locked at the sun.
Your second diagram suggests an axial-bond (From axle to axle) which will have completely different dynamics to your, prior, axle-facia bond.
It is absurd to suggest a spinning moon.
Now, exchange your ball for an aeroplane, facing right.
Hold your stick at arms length and, ignoring the earth's (You represent the Earth btw) rotation, start to rotate clockwise... You will note - The plane's right side ALWAYS faces you (the Earth) - BECAUSE it is NOT ROTATING on its own axis - it is NOT rotating at all.
Now, view this from many angles - Just a plane flying around and around in circles, NOT Rotating ONCE.