Are disconnected PV panels damaged when exposed to sunlight?
Excellent question and I cannot for certain tell you the answer except to say that I leave solar panels out in the sun regularly not connected to anything and they have not developed any damage.  I would be more worried about the connectors of your panels when not in use accidentally coming in contact with something connecting a circuit and causing damage or a fire.

I look at PV panels like a battery with a + and a - that when not connected to anything has a potential, but not utilized until the connected or a circuit is formed.

I would be more concerned about the "shady areas" and your fixed panels and the potential for hot spotting and damage from that.  Your panels should have bypass diodes, but if they are old, or if they don't have enough, your panels could be damaged (or worse, a fire) if they are partially shaded.  look up bypass diodes and hot spotting on goolge.

I am fairly certain that again, this phenomenon will only happen if the panels are actually in use and connected to a circuit.  So if the fixed panels are disconnected in the shady areas you should be just fine.  Happy camping.