You will see big signs at the rest areas of motorway AP-7 in Catalunya (the motorway from the French border along the Med sea) warning you not to leave valuables or anything in sight.
But I would take that as a general warning, applicable in Tarragona as well as in Vienna or Stockholm.

I have driven half your itinerary, i.e. from Málaga to Barcelona along the Med, and on other occasions many road trips through Andalucia and Southern Catalunya.
No problems so far, no "awkward" situations.

The hardest tasks was to avoid to (often really expensive) tolled sections of the motorways. It works pretty well between Andalucia and Valencia. But between Valencia and Barcelona, you have no real other option for most legs than the tolled AP-7 or the parallel N-340, a mostly two-lane highway with lots of truck traffic.

When you always have a car in tow, you may want to look deeper into options for accomodations, esp. when you want to visit the bigger cities. You will find motels along the motorways and - e.g. in Valencia or Barcelona - park&ride facilities to visit the city centers with public transport.

Great information, thanks! Does anyone have an opinion on whether one should rent or lease a car for duration of 21 days?

Not an answer to your last question, but I highly recommend you to go down from Granada to the Mediterranean coast along the scenic "Suspiro del Moro"-road (the Moor's Sigh). The name comes from the legenedary sigh of Boabdil, the last emir of Granada, when he at the mountain pass known as Puerto del Suspiro del Moro, for a last time had a look back upon the now lost city (1492). His mother shall then have said: "You cry like a woman over a city you couldn't defend as a man". http://www.holavalencia.net/2010/02/...and-almunecar/

Plenty of areas near/in valencia with free on-street parking. let me know if you need to know which neighborhoods those are.

might not get a car til i left sevilla.. unless you are going to take good advantage of it for small towns along the way.

I am always an advocate of renting a car.

We returned this week from Cataluña, drove a lot in back roads, going and coming back from Andorra and also around the Valle de Camprodon, ....frankly I cannot invisage a more pleasant driving, ...of course common sense is always needed in life. Good luck.