This past September we spent 3 1/2 weeks in England which included many of the areas you mention. We have taken many trips through the UK and other left-side drive countries and have had some experiences "switching" to the "wrong" side. Nevertheless, we found Devon and Cornwall difficult. The roads are very narrow and visibility limited because of the high walls and hedges. Definitely pick up your car outside of London. As we were arriving and leaving on a cruise ship, we picked up our car in Southampton. If you want to see the Cotswolds in a limited time, we recommend taking a train to Moreton in Marsh and booking the "Secret Cottage" tour (http://www.cotswoldtourismtours.co.uk/). This is a great way to see a lot in a limited amount of time without having to drive.
We do recommend booking places to stay ahead of time. If you want to drive, we recommend the Old Rectory Hotel in Martinhoe, North Devon - lovely accommodations and delicious food, out in the countryside. We spent 3 nights there and toured the north Devon coast from Ilfracombe to Dunster, visiting Arlington House and Dunster Castle as well as Exmoor.
In Cornwall, we rented a cottage from HomeAway near Mousehole for four nights. It was an excellent location from which to see everything from the Lizard, to St. Michael's Mount and Penzance and a few National Trust properties inland (Trerice and Lanhydrock). In spite of being reasonably comfortable with driving in England, we were tired and on the last day hired a private driver to take us to Minack Theater, Lands End, the Levant Mine, and St. Ives - a wonderful day and well worth the money. He drove us to small villages we would not have driven to on our own.
We had a wonderful trip and loved the area. Basically, our advice is DON'T over plan. Try to pick a few places to use as a base and not move about too much. Realize that driving can be tiring and will take longer than you expect.