Nick, I think that must be a typo: Cuenca--though a very interesting place--is not on the way from Salamanca to either Cordoba or Seville. Perhaps you meant Caceres? It's a great place, but I just don't see that there's time for a stop there.
Jaice, since you've explained you're considering a possible relocation to Malaga or Valencia, I think you need to drop Arcos. It adds 1 hr. 45 min. of driving time that day, and in Arcos you'll need to park down below the historic center and walk up. I don't think that's going to be just a one-hour stop. In your situation I'd want as much time in Malaga as possible.
Although I imagine Peniscola is a charming place, my feeling is that you either really want to see Barcelona or you don't. If yes, I'd drop Peniscola in a NY minute. If you're not all that interested in Barcelona (which I love), then I highly recommend dropping it from this trip and redistributing those two nights elsewhere, assuming you are not forced into departing from that city.
So much of this trip would be more easily done via express train. It's not like you really have time to wander off the direct route to see things with the car, unless you think a small town somewhere is going to be more interesting than places like Toledo, Seville and Granada. A big advantage of taking trains is that you can pack a nice picnic lunch and eat on the way, which can save quite a bit of time in transit--and you have a very large number of travel days on this itinerary.
For what it's worth, Valencia has rapid rail service not only to Barcelona but also to Madrid (via the aforementioned Cuenca, incidentally). The one indirect-by-public-transportation segment is Granada-Valencia.
Since your trip is coming up pretty quickly, you need to be aware of some sights for which you'll need to get tickets before the day you arrive in town, assuming you want to see their interiors. The urgency varies by sight; in many cases it will probably be OK to get the tickets online just a very few days in advance, but at least for the Alhambra, I think that would be risky.
These are the places for which we usually recommend people not just show up without tickets:
Granada: Alhambra (used to sell out months in advance)
Seville: Alcazar and cathedral. (See Rick's guide on how to deal with the cathedral.)
Cordoba: Mezquita (might or might not have a significant ticket line).
Madrid: Palacio Real might possibly have a somewhat-annoying ticket line; it wasn't a problem for me in 2015.
Barcelona: Parc Guell [update: ticket machine now at park], La Sagrada Familia, Casa Batllo, Casa Mila/La Pedrera, Picasso Museum and Palau de la Musica Catalana.
As you can see from that Barcelona list, a large number of sights in that city are so popular that you must get tickets ahead of time. Those are all timed tickets. It is impossible to figure out precisely how much time to allow for each sight, so there's a limit to how many you can prudently plan to visit on one day. This is one reason why I think you are going to have severe time problems in Barcelona. You're not going to be able to just take any random tickets you can get during your short 1-1/2 days in the city; some of the only-available tickets might be for overlapping time periods.
Edited to add:
I almost forgot this: You have many in-transit stops planned. You must protect the possessions you leave in your car. Spain has a problem with thefts from tourists' cars. All the valuables you aren't going to carry with you should already be locked in the trunk when you pull into a parking lot. Do not open the trunk at that point; someone may be watching.
I would have a backpack (lockable) or tote bag to carry with me. It would contain expensive electronics, cameras and anything mission-critical (like prescription medications). I'd have back-up ATM cards and credit cards in something like a money belt.
