"Two adults, each armed with an oyster. "

No, two adults each armed with a 7 day zone 1-2 Travelcard bought at a train station ticket office so they can use the 2-4-1 offers on daysoutguide.com. This means paying extra (as an extension ticket) to get to & from Heathrow and HCP. Windsor Castle is outside London and requires a separate train ticket. You cannot use Travelcards or Oystercard PAYG

oops - that should say >>Paddington trains change at Slough for WC.<<

"Two adults, each armed with an oyster. "

Sounds like a scene for Monty Python, a duel with oysters....

Just so you are aware I don;t believe there is any way to see both in one day using public transit. We did it - by car - leaving London very early in the AM - and not seeing everything at HC by any means - but it was all the time we had - since we were leaving for the Cotswolds the next day.

I do realize that. Thank you.

Go to Windsor from Waterloo, if possible. Reasons:
Waterloo to Windsor trains are usually air conditioned. Someone on board usually checks tickets. There are usually "quiet" cars with no talking on mobile phones allowed.

From Paddington, the local FGW trains usually don't have AC. Nobody checks tickets and you can get quite a rowdy crowd (or not, it's luck of the draw), and there aren't any quiet cars so there are usually several people talking loudly into their mobiles in every compartment.