I do not know of a day hotel, but have booked a tour with Alunsa Royal. The contact person is Arianna@netline.cl
She works at the Four Points Sheraton in Santiago. We are staying for a couple of days in Vina Del Mar and she has arranged for a driver/guide to pick us up at the hotel there, do a full day tour of the area, including Santiago and dropping us at the airport. Our flight leaves at the same time as yours.
Good luck. Hope this helps