I agree with the comments you received so far. I also would suggest staying in a hotel close to the train station (Atocha) rather than stay by the airport. I will also go so far as to say, depending on how you think your baby will fare after your flight, you might consider going immediately to Cordoba or Sevilla which does eliminate one of your transitions. I've traveled a lot with kids (I have 4). Personally, I think I'd rather stay overnight in Cordoba two nights instead of taking two train rides in one day back and forth to Sevilla. Additionally, Cordoba is a marvelous city that you could really enjoy at a slow pace with a child in a carrier or stroller. It has a beautiful river and bridge and is known for the homes with patios and gardens. The town just seems to be designed for lingering. I do like Sevilla a lot, but Cordoba is just calmer.
You might think about a day trip to Arcos from Sevilla though you need to know it will probably be quite quiet there. We were there at the beginning of November and not much was happening in Arcos, but it was a peaceful day for us with beautiful views. Also, there is a lot to do in Sevilla, so you may not need to plan many day trips, especially if you decide to make Cordoba a two night stop.
Likewise for Barcelona/Catalunya, I like the idea of staying in Girona at least a couple nights. It is a beautiful city with much to do, and as Acraven said, there are many options for daytrips from Girona. I especially enjoyed Besalu. Incidentally, I think you'd want a winter snowsuit for the infant. It gets fairly chilly in that area in the evening, esp for a child not doing any moving around. We were there at the end of December, and we needed some warm layers (and we are from MN!)
You have picked wonderful cities to visit and will enjoy yourself regardless of your final choices. I know you are thinking that you want to change hotels as little as possible, which is a good consideration, but also factor in backtracking and the amount of time being in the confines of a train. It's a personal choice and you know your own preferences and the needs of your baby.
I'm just thinking that some days in less busy towns might be welcome especially for baby.