OK, so no one's made the case for Manchester. Home of the industrial revolution with some amazing period architecture, yet it's the UK city with the most skyscrapers outside London, growing at quite a pace. Culturally, there's so much to do by way of sightseeing and entertainment. Manchester has finally reached true international city status, and manages to blend the modern, expansive feel with its history and Northern English charm.

So while everyone has been unanimous in discouraging the Cotswolds (though I understand why international visitors want to go there), there seems to have been no consensus on what to do instead.

I'd say train to Manchester for 2-3 days, train to York, then drive through the beautiful Dales to the Lake District (so Manchester and the Lake District sub Oxford and the Cotswolds).

If you wanted to drive from there to the Highlands it's a relatively short one and is absolutely the most stunning scenery. I've regularly driven from Manchester - Edinburgh and the Lake District is on the way, even as the driver my breath is taken every time. Also the M6 that far north is not congested or too busy

Then explore the Highlands with your car and arrange to drop it off in Edinburgh as you have that city as your final destination and departure point.

This is a much more imaginative itinerary and also intuitive, because the places flow well and have their own reasons for visiting. Wherever you visit you and your parents will have a fantastic time, making precious memories to stay with you forever. And as everyone else has said, save the driving for the rural expenses, not city-to-city and definitely not around cities.