Drive to Ikea and park for free at Bellevitge train station, then get a 10-min train to the centre, they're very frequent.
DH has a lot of experience of driving around Barcelona and even he finds it terrifying, they're bloody nuts. Even the train straight from Salou is a great option, about 1hr30, sit on the right for sea views, get off at Passeig de Gracia super-central, right in front of a Gaudi building.
There are toll roads, about €8-10 one way, train is €16 return per adult. You can get to Barcelona on free roads, but it takes abit longer and can be a bit disorientating if you don't have gps.
I'd recommend visiting Cambrils, Tarragona, Montserrat for a long walk if you have a sling for your DD. Some nice monestaries around: Poblet, Santes Creus, Siurana up in the hills (hairpins bends ahoy
) or Escala Dei in the Montsant for great local wine. Vilafranca del Penedes between Salou and Barcelona is Priorat wine region, all the vineyards have visitor centres and tastings.
You'll have a great time. Salou beach is huge and you can walk to Cambrils or cycle if you fancy an activity.