Okay, you have some idea of what it is like to travel with an infant. Even if you've been to Europe before and know how you'll handle jetlag, babies are different. You can't keep them awake for hours or put them to sleep too early.
I'll repeat what others have said. You are taking a risk by booking a flight on your arrival day at BCN. If there's a delay anywhere between home and getting to the gate for that flight, you could miss it and then have to pay a lot of $$$ for another flight, if you can even get one on the same day. Among the things that could go wrong - weather or mechanical delay, air traffic congestion or long passport control lines at BCN, waiting for checked luggage.
Second, travel by train takes time. It will take you time to pack, check out and get to the train station, then find and board your train. Figure 45 minutes to an hour (traffic ?). On arrival you have to get to your hotel, check in and drop your luggage before anything else. I just looked at the train schedule for a random day in September, Munich to Paris. The only morning train that's direct leaves at 6/22 am and takes 6 hours. All the others require a train change about midway. You could take the one at 7.46 (you may be getting up really early anyway because of the baby?), that gets to Paris just after 2. Maybe you are checked in by 3 pm. But you've been up since 6. That doesn't give you much time. The next train doesn't get to Paris until after 5 pm. There are 2 direct trains from Paris to Barcelona at about 10.15 am and 3.15 pm, take more than 6.5 hours. Basically, you lose the day to travel.
Day 1 - travel to City 1
Days 2-3 - see City 1
Day 4 - travel to Paris, a couple hours to sightsee before dinner.
Days 5-6 - sightsee Paris
Day 7 - travel to Barcenlona
Days 8-10 - sightsee Barcelona
Day 11 - fly home.
City 1, 2 days; Paris 2 days, Barcelona 3 days. Travel 4 days.
Backpackers or "power" tourists might enjoy a trip like that. Most of us here wouldn't plan a trip so fast-paced even with babies.