First off I want to thank everyone for all the wonderful posts. The information has been extraordinarily helpful!
I wanted to comment/reply to a couple of the posters concerns.
--London vs. Bath first: Honestly, I think we are more excited to see London than the other parts of England (since this is our first trip) and therefore, would like to work out the jet lag some other place so we have full energy for the big city.
--Driving the same day: While I totally agree this is less than ideal, it works best for the itinerary. I'm a physician, and regularly used to pull 30 hour shifts. Won't be a fun drive, but wouldn't expect too much trouble either. Will just have to take it slow, and get a cup of coffee along the way. Also, my kids tend to fall asleep rather easily in a car-I imagine that after all the hassle of the plane, they will sleep most of the way to bath.
--Big picture for why we are choosing Bath/Cotswolds is convenience. We are in England long enough to do something outside of the city, but don't want to have to go too far. Seems like this is a reasonable drive, with enough "highlights" to keep up entertained for a couple of days. Not too particular about this vs. that sight. Just want to see something other than 1 city.
--Kids: The kids are usually fine to do what we want, so while they are a consideration, we're not going to plan the whole itinerary around them, and certainly aren't going to spend the days at attractions (like playgrounds, etc) that we have in the States.
--Bath Itinerary: Neither my wife nor I are huge museum fans, but enjoy casual viewing-this works great with young kids, because we are fine to leave when they get cranky. In terms of specifics for the itinerary, we're not really dedicated to any particular places. Glastonbury sounds ok, but would be more than happy just to drive around and see some random towns-all depending on the mood of the kids and weather, etc.. Any helpful suggestions for towns other than Glastonbury/Wells near bath? Exeter? Bristol?
--Cotswolds-Will plan to get an Air BNB here and again, really don't mind if it's in Stow on the Wold (as folks have suggested) vs. Chipping Campden vs. some other nice town. Just seems like a nice idea to get a little house in the country and take in the scenery for a day or two. After hearing from folks will most likely skip Stratford-upon-Avon and do Warwick. Should be enough for a day.
--Cotswolds back to London: Again-thank you so much for the helpful suggestions. Sounds like Blenheim Palace and Oxford is way too much for one day. Any suggestions as to which one is better for the short excursion we have time for? We recently did Hearst and the kids did just fine there (of course the 3 year old twins really have no idea what's going on). So I think Blenheim would be possible, but sounds like if we had to choose-would be better to spend the day in Oxford.
Again, I want to thank everyone for taking the time to write in comments. It really has been enormously helpful for planning this trip.
All the Best!