My wife, 20-month-old, and I stayed in Silvia and Gabri's apartment for five nights and really enjoyed our stay. The apartment is in a quiet neighborhood in Poble Sec, a short walk to a nice pedestrian-only street with lots of good tapas restaurants. It's also a short walk to the metro and bus stops on Avenida de Parallel. It's very convenient to Montjuic, too.
The apartment is a nicely-renovated studio that feels more like a one-bedroom. It's up a couple flights of stairs, if that's a concern. The bed was comfy, and there were lots of amenities to make a toddler feel at home: crib, high chair, and toys. The kitchen was really well stocked, if you want to cook or eat in. The roof deck was nice, if you enjoy basking in the Catalonian sun or need to dry your clothes.
Silvia was very prompt and helpful in her communications, and check in was very easy. Thanks for a pleasant stay!