Having lived in Barcelona for ten years, this is one of the nicest places I've stayed at or visited. It is around the corner from the first apartment I rented in Barcelona, so I knew what to expect of the area. It is slightly away from the center but easy to get to anywhere because the purple line is fast and runs often.
The place was perfect for our two families with one kid each, the rooms were just the right size, and the host offered to put in cribs and high chairs.
The living room is long but not very wide, which was fine for us as we didn't hang out much in the apartment - that's not what Barcelona is for. It's sobre-atico, so high up and quiet, and the small balcony is a nice touch giving a 180 degree view over the city.
I always look for one suggestion to improve the place, so here is mine - the water temperature in the shower is not very stable. It can go from just right, to cold, to scalding hot, without touching it. The house rules mention that the shower should work fine if only one person at a time showers. I worry that the owner has dismissed earlier reports of the shower not working correctly by assuming it's because multiple people are showering, but that was not the case for me - I was always the only one in the apartment to shower, and it still happened. I suggest the owner takes another look at the shower problem. (And as a side note, it is entirely possible to have a shower setup where multiple showers at a time can be independently active, so I would even suggest to just fix it properly all the way).
This is a minor detail though for a short-term stay apartment. The quality of the apartment in general is so good that this was a surprising defect, because the showers themselves are spacious and nicely looking and maintained.
Would not hesitate to stay here again!