Need to know when you are traveling as this may impact the amount of time available to visit within a destination. Also, is this a first trip to Spain? Strongly suggest you gather information, but make other travelers take active role in selecting the intinerary.
14 nights and 6 destinations, obviously you enjoy lugging, unpacking and packing luggage. Plus you must enjoy meeting new hotel desk clerks and spending time transistioning from place to placet.
You really have an intense stress potential first itinerary.
Lets step back and ask "is it important that you SEE as much of Spain as possible?" Or "is it important that you EXPERIENCE as much of Spain as possible?"
There are so many wonderful memories to be gained by designing a trip seeking experiences.
Here are some suggestions:
Arrive in Barcelona and spend 4 nights w a day trip.
AVE train to Madrid (wonderful convenient method of travel offering scenic views and arrives near old town madrid)
Stay in Madrid for 3 nights w a day trip to Toledo (I have downgraded Toledo for has become massive tourist jam). Spending a night there is highly romantic and provides a different glimpse of the city. Just not sure if this is a must do for you.
AVE from Madrid to Seville for a 4 night stay. Delete day trip to Jerez and Cadiz and insert daytrip to Ronda. You can also hop on and off the AVE for a couple hours to spend in Cordoba while on your way to Seville (highly recommend this option).
Take a bus from Seville to Granada (less than 3 hour ride and quite comfortable). Spend 2 nights in Granada.
Train back to Madrid for departure home (means buying an open jaw airfare, quite common).
So now you have 14 nights and only four room changes.
When staying in one location for three nights or more we always first seek to rent an apt. Advantages are costs, more room, kitchen, we always seek a terrace/balcony, sometimes offer a clothes washer and we find to be a more rewarding experience. Check out Airbnb as a start for examining these options. FYI we have never had an unsafe experience in an apt.
To answer you questions: we rent cars due to our desire to explore, but advise aganist not renting a car to get from point A to B. Our daughter last saturday night took the night train from Barcelona to Granada (where she is "studying" this summer) and enjoyed the experience. She is young and wanted this experience. We would fly and pay more money in order to save more time.
TIP: pack far less than you think you need. Pack even less than what you just thought of. Success? Three carryon bags are all you need between three travelers. This really does impact your trip.
Want to save money? Walk a short ways outside the main tourist zones to eat. You will be astonished at the price differences. Be adventurous w eating. Dont know the language? No big deal.
Finally, take out a map and plot the distances between your destinations. Then use a map of the USA and plot equal distances to gain a perspective of how far you are traveling. Use your home city as the starting point.