As I understand it CP (Camping Tyres) have stiffer side walls to better cope with a lot of time spent not moving and the generally higher basic weight of MHs
Oft repeated but not the case; a CP carcase supports a higher pressure than a C carcase and it is this pressure which supports the motorhome weight, rolling or stationary. The only tyres that I know of where the sidewall construction is designed to carry weight are car runflat ones.
A Michelin Agilis CP tyre for example, being one of Michelin's GreenX low rolling resistance tyres, has one of the 'floppiest' sidewalls you're likely to encounter on a tyre in that size. I once cut cross sections of a Michelin Agilis CP and a comparable C tyre (I recall it was a Falken Linam R51) and the C tyre's sidewall was markedly thicker and stiffer - designed perhaps to survive white van man driving it up kerbs..