Makes sense. My permanent office is in London. Once every couple of weeks to Nottingham should be fairly clearly not 'commuting' notwithstanding odd government definitions
Same understanding as me. If I do business miles because it suits me (rather than the company) to, say, drive to the airport rather than getting a car or the train then I apply the round-trip mileage against my tax return.
I agree with Andy, better the devil you know than the one you don't. Swapping cars can sometimes be a false economy. I'm almost tempted to keep mine now we have a Ghibli on the fleet.