Are we insane?

As mentioned a few days ago, we've planned a trip to Spain in a couple of weeks. We weren't sure where to go, but realised that we both love Spain and so thought it would be an ideal place to go since we can get direct flights, we have friends there we're hoping to see who also just had a baby, and it seems like a baby-friendly place. But now that all the arrangements are in place, we're wondering if we were out of our minds to plan the following itinerary:

Fly to Madrid (first flight!)
Spend two nights in Madrid, hopefully visit friends
High-speed train to Sevilla
Spend three nights in Sevilla
Train to Granada
Spend two nights in Granada, visit the Alhambra
Rent a car, drive to Marbella
Spend two nights in Marbella
Drive to Malaga Airport
Fly home from Malaga

So that's four hotels in nine nights. With an infant. In what will likely be temperatures around 35C/95F (which Spanish friends warned us about at dinner last night). With lots of luggage. In a country where dinner doesn't start until at least 9:00pm. Where breastfeeding in public is evidently not really done.

It all made perfect sense when we were planning it, but I'm starting to wonder, are we crazy?