Spain

No child, but we did the same pickup in February. Ours stopped twice. Once on a side street near the Sagrada Familia and once up on Montjuic where there is a cafe with proper toilets. He asked at the start how long we wanted to be out of the car rather than deciding for us. Of about an hour and a half in total, maybe 40 minutes was spent standing outside somewhere.

I would not do it. Two hours of city tour with a child who has been up since four is two hours nobody enjoys and you still arrive at the flat wrecked. Left luggage at Sants is a few euros a bag, and Gracia has shade and a fountain at Placa de la Virreina where a five year old can run about like a lunatic for an hour while you sit down with a drink. Costs you almost nothing.

Four things that worked when mine were that size and we landed into heat. 1. Ask for the booster seat when you book, not on the day. Seat rules are taken seriously here and arrivals is a bad place to be sorting that out. 2. Buy two cold bottles airside before you board. You land with them and you are not queueing at a kiosk with a crying child. 3. Put the stops at the front of the run. By three in the afternoon the paving at the Montjuic viewpoint is roasting and there is almost no shade at the rail. 4. Get the key handover confirmed in writing before you fly. That is the bit that goes wrong for us, in every country, every time.