Looking for suggestions on how best to do this that includes golf cart and guide and visit to hamlet along with possible pick up and return to paris
I see a few at Get Your Guide that meet most of your wish list, except the golf cart. When we did this 10 years ago, the golf carts could not be reserved. You just signed up when there, and when a golf cart became available, you got it. We did not take a tour, just went out on our own by train, so we were on our own schedule.
We did not use a guide or tour. It is, however, very easy to take a train to Versailles and back. The palace is a very short walk from the train station in Versailles. Sorry, but we can't help with the golf cart information.