I agree with spending the time in Spain. There is much to see in Portugal, and the ground-transportation links can be challenging.
I like Ronda a lot, but I'll leave Andalucía to others since I haven't been there recently.
I also can't really address the car-vs.-train question since I've never rented in Europe, but I think a good bit depends on your ultimate target list of bases and day trips. Keep in mind that you can get from Barcelona to Madrid considerably faster by train than by car, and with no parking issues to think about. Ditto for the Madrid-to-Seville relocation. And if you plan to make sightseeing stops along the drive from one hotel to the next, you must be very careful to keep all your belongings hidden in the trunk. I have found the countryside around Madrid generally pretty dull.
With the caveat that I am almost exclusively a May-to-September traveler and can't speak to how lively these places might be in April...
Possible side trips from Barcelona (though 5 days is short just for the city itself):
- Girona: Worth at least a full day, plus it's a good base for Figueres, Cadaques and Besalu; has a large, atmospheric historic center, two interesting cathedrals, a walkable wall and a quite good art museum. Seriously, consider it as a possible base.
- Montserrat: Check other sources; I didn't have time for it. Also consider weather since it's up high.
- Figueres: Dali Theatre and Museum
- Cadaques: lovely white town with dripping bougainvillea (well, in the summer anyway). Dali House is in a nearby village, walkable.
- Besalu: small medieval village with a fortified bridge. A quick-visit sort of place that might be utterly dead in April (or not).
- Sitges: artsy beach town with at least one good museum. South of Barcelona.
- I could say positive things about Puigcerda and the surrounding area, but that's up toward the Pyrenees and I think not a great idea so early in the year.
Possible side trips from Madrid (after Toledo, my #1):
- Segovia: aqueduct, plus other sights. I found the architecture interesting and just wandered.
- Cuenca: shortish trip by AVE that will be affordable if you buy the train tickets when the initially go on sale; otherwise too expensive, and regular trains are far too slow. Lots to do here: medieval hill town with two good modern-art museums (over 1 hour each for me), a cathedral and hanging houses along a ravine. See it before the other American tourists discover it.
- Salamanca: handsome university city. Large historic area.
- Avila: To me it's just another wall and imminently skippable.
- Alcala de Henares: another university town with a very pretty historic district. Visually, I thought it was more attractive than Salamanca, but that's a matter of taste.
For your free time (assuming you don't just alot it to Madrid and Barcelona--that would not be a mistake): East of Cuenca are a couple of interesting places, only one of which I've managed to visit. With a car, they could be combined with Cuenca. Teruel is one of Spain's most isolated provincial capitals. It's known for its Mudejar architecture. Quite non-touristy given its attractiveness. With public transportation I think the best connection is by train south from Zaragoza (also interesting). Teruel is at altitude so could be chilly as well as windy in April. The small town of Albarracin has been on my radar for ages, but I don't think it has any public transportation.
Alternatively, there's more than a day's worth of good sights in Toledo, so you could spend two or three nights there. I stayed 3 nights and was happy with that decision.