We stayed in Deisi's flat with our two children of 3 and 6 years for a week in March. Ana, the cleaning lady, was waiting for us when we arrived. The flat was very clean and perfect for our little family. We had a very positive experience in all ways. Deisi was very helpful before our arrival giving us advice concernant our transport.
Finally, we decided to go by Easyjet from Nice and from the airport to the center by train and metro. You really do not need the car when you stay in Deisi's flat in Passeig Sant Joan - not even with children - as the metro station (Verdaguer) is only a 100 meters away. The transport from the airport to the center (Sants estacion) is very easy too as the train leaves every 30 minutes and takes about 20 minutes. You can buy a ticket T-10 (10 trips for 10€30) that can be used in the train as well as in the metro.

Futhermore, the flat is situated very close to la Sagrada Familia (10 minutes walking) and a thing our children loved was the three playgrounds in Passeig Sant Joan:)
We are looking forward to going back very soon!