Agree with others above, you won't find much in the way of Civil War sites in Barcelona.
Alternatively, the Aragon region was a pivotal battleground during much of the Civil War. The capital of the region, Zaragoza (3 hours drive west of Barcelona) is a good base for a few days just to explore the city itself and then make daytrips out to Civil War sites like Belchite. There is a Spanish Civil War Interpretation Centre just north of Zaragoza, in the village of Robres.
Since you will have a car, you may find interesting to actually follow the George Orwell route in the Aragon region. On the route you will find the very places that inspired his book Homage to Catalonia, like Monte Iranzo battleground, Tres Huegas bunkers, and the Santa Quiteria Hermitage.
You can read more about the route here: https://www.spain.info/en/discover-spain/george-orwell-route-aragon/