Thanks everyone who responded so far! This is all really helpful. I will look into the possibility of doing France week 1. A potential complication for that is that it would push us to London on week 2 of Wimbledon and I'd imagine the tickets are harder to get then. I had researched "The Queue" for tickets, which seemed like a pretty safe bet for getting something on the first few days if you arrive decently early. I'm not sure about later days, which I'd guess would be a bigger challenge to actually see tennis. We know from the U.S. Open in NY that the first days of a grad slam are really fun with so many matches happening all over the place that you don't need tickets to the main courts. That said, if I felt confident in getting in with tickets to main courts, week 2 has the advantage of better matchups. Maybe I should ask on another thread (or tennis forum) about week 2 Wimbledon tickets via the Queue.
The suggestions on reducing time in Bath and Cotswolds are helpful and reinforce what we were already thinking. We were considering skipping Cotswolds entirely. For Bath vicinity, the kids definitely want to go to Stonehenge and Avebury (and they have really liked the most comparable places to this we have visited elsewhere). They are also excited about King Arthur and Holy Grail stuff in Glastonbury/Wells, but have little interest in Bath itself. They also seemed not particularly interested in the Iron Bridge Gorge part of the Rick Steves itinerary, so we were considering cutting that too.
We all like outdoors and castles, so Northern Wales seemed appealing, but reading about recent mobs of people at Mt. Snowdon over Easter weekend, that is making me second guess whether that really feels like good outdoors experience or ruined by being overwhelmed with littering mobs. (There's a tradeoff. Mobs at Yosemite are fine because it is so amazing. And generally, if you hike more than 30 minutes from a road, people thin out.) We also were thinking we would spend more time than suggested by RS around Glencoe to do at least long "Scottish highlands" hike.
I'm also curious about thoughts on Loch Ness, which from the outside sure feels like the type of place people go mostly because others will ask if they went. My kids aren't pulled in by the Loch Ness monster stuff. Inverness has some pull but also tempting to skip all that and cut down from Glencoe through Stirling to Edinburgh rather than head any further north.
Also, even though my family has already been looking through the RS France book, if there was an alternative use of the 4th week that was enticing enough, they would consider it. The most obvious is to just slow everything down in UK, but I think they'd vote for 1 week in France over that.
Putting this all together, if we did Northern France first, I'm curious on thoughts on this plan: Follow Cynthia's advice to stay one night at the Sofitel at LHR while exploring London before flying to Paris -> visit Paris -> then rent car for Normandy -> then take the car via ferry from Cherbourg to Portsmouth -> then do UK itinerary starting by staying somewhere between Portsmouth and Stonehenge (maybe Salisbury?) rather than Bath -> then modified Rick Steves UK itinerary, eventually returning car in York before train to London for final leg.
Or would it be better to loop back to Paris after Normandy and then fly to someplace like Bristol (where we'd rent a different car)?