The painting was the last major work completed by Van Loo, and he too was dead by the time it was exhibited at the Paris Salon of 1765 (these annual or biannual exhibitions, known as salons, were the place major works were traditionally first exhibited, before going off to the private collections of wealthy patrons). It was not his first attempt at painting this subject, but a previous effort a couple of years earlier had been so roundly criticised for not being sexy enough that he destroyed it and there is only an oil study remaining of the original version.
Probably not the de Nesle sisters, and definitely not by Jean-Baptiste Van Loo.
The de Nesle sisters became notorious because of their association with the young libertine King Louis XV. They were, one after the other, his official mistresses, in the days before Madame Pompadour and Madame du Barry. They were grasping and manipulative, out and out gold diggers, but he enjoyed their company and probably had a genuine passion for at least one of them. Their only tenuous connection to Chenoceau is that they were the grandnieces of Laure Victoire Mancini, the second Duchess of Vendôme, whose husband inherited the chateau in 1665 and whose portrait hangs in the same room at Chenonceau. Their mother's lover, the Duke of Bourbon, acquired the chateau in 1720 and over a period of 13 years sold off all the contents before selling the estate to Claude Dupin.
I don't think the sisters would ever have set foot in Chenonceau, but it is a beautiful painting which is clearly more about erotic love than the rather more high minded ideals of the Graces, and I am not surprised that each subsequent owner of Chenonceau has allowed it house room.