Driving in Spain

I have never been to Valencia, but have driven to and from Granada. The roads are good and once you are outside the cities, traffic is light. The roads are just like their counterparts in the rest of Europe (autovias, regional roads, and small routes). Granada itself is tough to drive in - a lot of the center is restricted to only taxis, busses, and residents. The Albayzin is very narrow and makes driving difficult - but it's doable, I've done it in a normal size car. It's easier to leave your car in a garage outside the center and get a cab in, unless your hotel has detailed instructions and parking. The Alhambra has a parking lot that is easy to get to - no need to go through the city to get to it.

The highways and medium roads out of Granada are good, and if you want to go south to the Alpujarras or to the coast, no problem. North towards Madrid and Toledo is boring but very easy. I would be extremely surprised if the route to Valencia was any different.

I just looked - Granada to Valencia is listed as 5.5 hours, and seems to be on A roads(major autovia routes) the whole time. 5.5 hours might be accurate if you don't stop and don't have any delays, but plan on more like 7 hours with short stops, longer if you want to get out and see more along the way. If you are good with that long a drive then I don't think you'd have any problems.

I haven't driven that route but outside of the cities, highway travel in Spain is very easy and not unlike the US. Speed limits are strictly enforced by cameras. An international drivers permit is legally required to drive in Spain.

Valencia is a great city and well worth a couple of nights. I think you will enjoy that plan. The train from Valencia to Barcelona is long but fairly scenic and convenient.

I also would have no concerns about driving. You'll want to find a parking lot outside the city center of Granada, unless your hotel can provide space and driving directions. (Rick's intro to his Granada guidebook chapter has a few tips.)

It's also possible that, by October, the railway construction near Granada will be completed and train schedules will improve. No way to know until that actually happens, however.

The autopista and main highway routes from Granada to Barcelona are very good, but tolls can be expensive. I have done it in a day (with a friend driving), albeit a very long day.

It is a sound plan though that you suggest ...
Day 1 Drive via Baeza/Ubeda to Valencia
Day 2 Explore Valencia
Day 3 Train to Barcelona (via Tarragona ??)
I am not sure if luggage storage is available at Tarragona station, but the following trains would let you see some of this once Roman city as well.
EUR 1282 / Dep 08:22 VALENCIA JOAQUIN SOROLLA (Spain) / Arr 10:40 TARRAGONA (Spain)
EUR 1152 / Dep 17:13 TARRAGONA (Spain) / Arr 18:10 BARCELONA SANTS (Spain)

Use viamichelin.com . I put in Granada ► Valencia, and got 6+ hours driving time (not counting pit stops, delays, etc). The estimated cost is about €86 for petrol, or €50 for diesel. The routes are inland, no coastal roads at all. The train takes 6 hours - though because of the track upgrades around Granada, Renfe provides a bus from the Granada train station to Antequera to connect to the train to Valencia. When you add the additional cost for car rental for 2-3 days and parking in Granada, it looks cheaper and easier to return the car when you get to Granada and then take the train.

There is definitely enough to occupy you for 2 days in Valencia.