When we were in the south of France in August one year our kids were overheated, one fainted and we just spent the day in the river up to our necks, wearing hats. I said to myself this is ridiculous, where's cool? Oh, I know. the Alps. So we upped sticks and drove back northwards to the Alps. I had bought a digital thermometer and had a probe sticking out the window as we drove along. It was 43 C when we started, and hard to breathe. When we got up to the foothills of the Alps the temperature dropped to 38, and we could start to breathe easier.
Part way up the Alps we saw an Aire, with pictures of tents and caravans crossed out, and a picture of a motorhome with a tick. That was the moment when I decided that a campervan was preferable to a caravan and haven't wanted a caravan since.
So my preference would be that if you are too hot, get in the driver's seat and go somewhere cool or jump in the river. Or spend the middle of the day in a supermarket, that's another option. My current mh has a built in air con and I have never used it, and don't intend to. For one thing it requires 230v which means being on a camp site and paying and for another, it weighs 38kg which equates to the potential to carry 38 litres extra of water.
I must admit though that this idea of a split air con looks good - but of course you will need some storage space to carry it around and it will reduce the living area when it's set up.