One way to do all that you mention is to travel by train from London to Stratford-Upon-Avon and stay there for two to three nights.
To do the Cotswolds justice, you need to devote a full day to the Cotswolds, at a bare minimum.
To do Stratford-Upon-Avon justice, I would do a full day there, seeing Shakespeare's birthplace and walking around town.
We spent three weeks in England in May of 2016. The highlight of our entire trip was the day we spent on a tour of the Cotswolds on the "Go Cotswolds" Tour, hosted by Tom. We were staying in Stratford-Upon-Avon, where we were picked up at our hotel in the morning by Tom and his mini-bus. Several other tour members were already onboard. The mini-bus seats 16 passengers comfortably, so you are not with a huge bus load of people.
We went to Chipping Campden, Broadway Tower, Stow-On-The-Wold, Bourton-On-The-Water, and the Rollright Stones, to name a few of the stops. Tom gave out walking maps in some of the towns, and made recommendations for shops selling coffee and cakes, or lunch. Plenty of time was given for us to walk around and take photos at each stop.
Tom was born and raised in Stratford-Upon-Avon, so he knows the Cotswolds quite well. We enjoyed his stories and explanations of local landmarks. Being a local, Tom can also suggest some great restaurants around Stratford-Upon-Avon.
Tom has a great personality, and keeps the whole trip fun! Not a dull moment!
Tom runs tours of the Cotswolds on Wednesdays, Fridays and Sundays. Priced at £35 per adult and £25 per child (under 16; under 3s go free). You will be picked up from your hotel, or from Warwick Parkway or Leamington Spa rail stations, if you choose. Tours start at approximately 9.15am, and finish at approximately 5pm for a full day’s Cotswolds adventure. Once a month, Tom also runs a pub tour of the Cotswolds. Pick up is also possible, on Sundays, from Moreton-in-Marsh rail station.
"Go Cotswolds" Tour is highly rated on TripAdvisor, and has just received the Trip Advisor Certificate of Excellence for 2016!
Contact Tom through his website, and book a fun day tour in the Cotswolds. http://www.gocotswolds.co.uk/
Click the red "Book Now" button on this page to sign up for the tour.
http://www.gocotswolds.co.uk/tour-details/
Or contact Tom at phone number 07786 920166 or email [email protected].
Also see the following page, "Joining a Go Cotswolds Tour From London and Birmingham" to see how to do just that:
http://www.gocotswolds.co.uk/blog/joining-a-go-cotswolds-tour-from-london-and-birmingham/
Stratford-Upon-Avon is a lovely place to spend a couple of days, in case you & your family are looking for a day or two away from London!
Have a great trip!