We spent a week at Marta's and we left with mixed emotions. The apartment is located perfectly, it's really minutes from the beach, the bus stops at the corner, you can be in the inner city in 20 minutes, or you can walk in on the beach in less than 45 minutes, even with a stroller. The street is full of restaurants, shops and bars, we had great tapas just across the street. The apartment itself is nice, the baby's room is amazing. The kitchen is fully equipped, you can really feel like being home. We even tested the heating and it worked out perfectly. Marta and her sister are extremely nice and really really helpful.
The only problem we had was with a neighbor. I know that it's completely out of Marta's hand, but we suffered a lot from it. The neighbor above if watching TV all day (from 9am) on full volume. Literally on max. You cannot rest for a second. We had nights when the noise was intolerable till 2am. Marta made everything possible to make it stop and so we could enjoy two evenings without the noise, but all other nights and days it was a disaster.
I'm sure that Marta will do everything to have the situation fixed and when she succeeds we would call it the perfect spot in Barcelona when traveling with a toddler. Until then it's still the perfect apartment if you stay out late on the town anyway, or you bring the party home.