Is there a motor home to suit this . . .

Have seen some in magazines that have an outside run that is colapasble they simply put it up when camped and allow the cats into it. Have been told that overseas it is not unusual to walk cats on leads good idea, good exercise for the moggie and the human. There are pet loos that are available artificial grass area wash it out so that would cut down on carrying and disposing of kitty litter. As for leaving the animal inside on a hot day i take the motorhome would have air con so as long as you have the power source no problem. Customising a motorhome to suit shouldn't be a real problem they are just plywood and other bits a half decent tradesman would be able to shape it how she wants, most off the shelf motorhomes are designed with travel with humans only in mind, but can be changed around to suit. Probably help if you had a budget stated so it is apparent if a new build customised to what she wants or a remodel would be the go also what size van she is comfortable driving, some of Ford or VW transit vans if not wanting anything to big would be easy to set up.

She need to find if the cat likes travel or is distressed by it. Each cat varies in its response to travel.
Some cats will howl and claw at everything in sight when they are transported - because cats are territorial and some get very fearful when being moved from home territory.

Other cats are comfortable with being transported and will settle down rapidly.
If she has the first type, travelling with it will be traumatic for both her and the cat.
She then runs the risk of the cat making a break for it at the first chance and returning home on foot.
Cats have been recorded as travelling several hundred kms to return to the place they know as "home".

Even dogs will do it. My parents, who lived at the area now known as Nollamara in Perth, gave away a young pup in the late 1940's to some people at Mundaring, in the Darling Range.
They returned home, and were awoken the next morning by scratching at the door. It was the pup!
He'd escaped shortly after they left Mundaring, and he spent all night travelling back to Nollamara!
Everyone was stunned at the distance he'd travelled overnight (around 35kms).
He had to cross the Swan River, so he must have travelled back via the road that my parents took.

Apart from the obvious heat problems, having animals may restrict places you can go.

No animals in National Parks, not even allowed to stop if you have them in the vehicle, quite a lot of van parks dont allow them and as mentioned if they do get out bird life can be in danger.

What about those cat or dog traveling cages, provided it will fit through the RV door? This could double as the cat's refuge (cage open), and as the place to tuck the cat away (door closed) when required. I don't know if there is a collapsible version available though.