Sorry for the delay. Not sure when your flight is. But since we discovered the issue the issue a few weeks before the flight, it definitely helped. I called just about every department in Alitalia and got nowhere. We were dealing with a few thousand dollars at risk because they didn't offer a free change or refund either. Gave some money to tzedakah and filed a detailed complaint with the DOT. The DOT responded that this does not violate any of their rules but they have forwarded the complaint to the airline and they will respond directly to me. B"H a few weeks later, the airline got back to us that they have agreed to confirm the infant on the flight as they have not found any other alternative.
If you still have some time ahead of your flight, I would suggest that you try the DOT too. (don't forget the donation to tzedakah...)
any idea what will happen if I just show up at the airport? I Just discovered I have the same problem-chase called to let me know-, But my infant does show up on my alitalia booking page. I'm going to try DOT, but If it doesn't work, what will happen at the airport?
update:
According to chase They took care of it. Alitalia claims they had accidentally double booked another lap infant. they removed the duplicate, freeing up the last infant space for me. Wonder what the odds that that's true...