The full name of the park is Reserva Natural de la Laguna de Fuente de Piedra and it is about a 30 minutes drive outside of Antequera. Laguna Fuentes is in a completely different part of Spain.
The N-432 is probably the most direct route between Córdoba and Granada, but I know of no castles along it. West of Córdoba is Castillo Almodovar del Rio Castillo de Almodóvar. Between Granada and Antequera are Castillo fortaleza de Archidona and Castillo de Iznájar. I recently read about El Torcal de Antequera Paraje Natural Torcal de Antequera. It’s not very far south of Antequera and has interesting rock formations.
Somewhat near Granada is Castillo de La Calahorra, but it’s really out of the way for the rest of you itinerary. South of Granada is Castillo de Lanjarón, but it’s more a ruin and is also out of the way for where you’re going.
About the same time as your trip, we too will be in that generally vicinity and visiting some of the same places, but our trip will be 25 days long and in a smaller geographic area. In Ronda, Córdoba, and Antequera we have reservations at the Paradors. I’m not sure if they are within your budget, but consider checking them out. We too will be in Córdoba for three nights during the patio festival.
As for driving tips, the historic center of Córdoba is a pedestrian only zone unless your hotel is in it. Part of Ronda is now a restricted driving zone. I haven’t driven in Sevilla or Granada since 2011 and 2014 respectively, and they were a pain. Once outside of the cities driving is a breeze.
I assume the cave you’re referring to is Cueva de la Pileta. It’s about 30 minutes southwest of Ronda. Ensure you check its hours and be aware there is a short walk between the parking area and the cave entrance. Also, the walk to, and in, the cave isn’t always level.
If you have any specific questions you can send a private message.
EDITED: I did some checking and along the N-432 route to Granada are the following castles: Castillo Ducal de Espejo, Castillo de Castro del Río, Castillo de Baena, Castillo de Luque, Castillo de Alcaudete, Fortaleza de la Mota, and Castillo de Moclín. I haven’t been to any of them and each looks different from the others. You’d need to look at each and decide which to visit. Keep in mind that many castles in Spain are privately owned and not open to the public except during certain celebrations. Depending on their uniqueness, some may only be worth a quick drive by for a couple photos.