The router address is 0.1, but I'm sure that my laptop's address has been this many times in the past
That, sir, would be an IP address conflict, and things become very unhappy if it occurs! So I think it's your
drug-addled rock star past catching up
with you!
why my laptop happily using said router is turfed off it's address unceremoniously when any other allowed device connects to the local network
I'm not sure exactly what you mean - do you mean you lose network connectivity when another device connects, or just that you don't get the same IP address every time you power up your laptop?
SD