HI, My family was planning a road trip the same week in Spain too. We chose the north as it is cooler, and in the north at this time of year, it is essential to book rooms as not to become stranded, especially with a baby.
We were originally going to go south but I think it will be too hot. You may have more flexibility in the south at this time because they consider this their relatively slow time because of the weather, except in major tourist cities like Granada. so you may have luck not booking in advance. Good luck, your itinerary sounds great!