Now let us suppose the squirrel is at the same distance as the man.

Has the man have gone around the squirrel and the squirrel around the man?

If it's only radii less than the other, where is the limit?

To get it I think I have to re-frame it like this:

If you hold out an object toward the centre, you clearly go around it when completing an orbit.

If you keep extending that to the origin but then go beyond, so your arm is longer than the radius, then you still go around it, until your arm reaches twice the radius.

Pick the sun as reference: the moon rotates. Pick the earth as reference: the moon rotates. Stand on the moon and pick any star as reference: the moon rotates.

From which reference frame would it not rotate?

1. Unlike position and velocity, which are relative (there is no given "origin" for them, no way to say where a thing is or how fast it's moving except relative to other things), rotation is absolute. A thing is either rotating or not, regardless of its relation to other things. Objects that rotate "experience (centrifugal) forces as a result" or "require (centripetal) forces to hold them together" depending on how you choose to describe it. This is detectable: hook two weights together with a newton-meter in space - and the newton-meter will read non-zero when the assemblage is rotating, zero when not. The reading tells you how fast it is rotating regardless of any external reference point. (An equivalent device to detect position or velocity is not possible, but it is for acceleration.)

2. Yes, everything "at rest" on earth is in fact rotating at the rate the earth rotates. If you stand on the equator at midday and do not rotate you will be standing on your head at midnight.