international driver's license required to rent a car in England?

Not an "international driving licence" but an International driving permit, which converts your licence to the language of the country that you're hiring the car in. As you're from the US with a licence in English (almost :-)) it's unlikely you'll need one.

I looked this up for our visit in a few weeks, and it appears the answer is no.

https://www.gov.uk/driving-nongb-licence/y

Your WA drivers liscence will suffice.

Rented before I left the States.

Picked up and dropped back off at Heathrow. Caught the shuttle to the rental office.

Reserved with Auto Europe because of the rate. Went with a compact. Clutch. First car was a Vauxhall that I had to swap out. Previous driver had burnt out the clutch. New car that was provided was a Renault. No problems. Very comfortable car.

An IDP is not required for US drivers in Britain. However, I always recommend it because the IDP does validate your state license. Believe it or not, I was actually asked for one by a rental agent in England because they couldn't figure out my Illinois license expiration date.

We recommend booking your rental car ahead to get your preferred mix of size, features, and price. Otherwise, you might get stuck paying more for a larger car or not getting an automatic transmission, if you want that. AutoEurope.com is a good place to get a price quote as they work with several vendor and they try to make all their info clear. The UK is not one of the countries that requires the IDP. Try to get some sleep on the flight over. See more advice at https://www.ricksteves.com/travel-tips/transportation and at https://www.ricksteves.com/watch-read-listen/read/articles/driving-in-great-britain-and-ireland.

How difficult is it really to drive on the opposite side of the road? We will only rent after 3 days in London (so we'll be rested) and out of Bristol through the Cotswolds return to Birmingham. I don't want this to be a stressful situation for my husband (or me!)

Not that difficult. The big problems most Americans report are (a) using roundabouts and (b) centring the car on the road so you don't scrape the near side on the curb or hedges/walls (country roads can be narrow.)

Make sure you pre-book an automatic, as they're not the norm in the UK.

First priority is reserve for best price. A note about AutoEurope: I don't care for them since adding a middleman increases the chances for a screw up, but if you do use them note that you are adding another non-refundable element to your trip that you will need to deal with if you cancel or get delayed.

Second priority is to reserve an automatic.

Third priority is to get a small car for ease of parking and navigation of narrow roads. Smaller than a Corolla.

Without question skip the IDP, that's a racket. Like getting a yellow fever vaccination before your visit-- so unlikely to be of any value it's not worth the trouble.

Some info courtesy of TA:
https://www.tripadvisor.co.uk/ShowTopic-g186338-i17-k6722631-Driving_in_the_UK_for_Americans-London_England.html

http://www.britainexpress.com/driving.htm

How difficult is it really to drive on the opposite side of the road?

While it seems a bit scary, once you are in the car, it becomes very natural to keep oncoming traffic on your (driver's) side of the car. Round-abouts are tricky just because roundabouts are tricky - it can be challenging to keep track of which exit to take on large ones. Some people lose some of their sense of where the passenger side is relative to the roadway, but its not hard if you are a fairly confident driver.

I found the hardest part is navigating. Have a good navigator with you or invest in the GPS if offered. It is well worth the price.

Don't do this..........https://www.youtube.com/watch?v=gngODTnc7Ec

Bookings made through the consolidator Auto Europe are pre-paid. They're fully refundable up until 48 hours prior to your scheduled pick up time but cancellation or changes after that incur a fee of $75. If you book directly with a rental agency, you don't usually pre-pay. Always read all the fine print.

I always book a standard transmission car. They are much less expensive to rent. Oh, it helps that I have driven a standard transmission car for 50 years.