It may look like that, but that's probably not what the ticket shows.

Whenever I have a disruption on a ticket, the old/cancelled section hangs around in the ticket - so you can see a full history of the ticket, rather than the ticket's current configuration.

The only thing to worry about is if the "correct" name drops off the ticket, leaving you with just the "incorrect" name.

(And without knowing the nature of the spelling error, it's highly unlikely that you even needed to bother having it corrected)

if you can't check in online would that really be such a bad thing? Presumably, with an infant, you are travelling with checked luggage - and I would even have thought that it may be a requirement that pax booked with lap infants would have to check in at the airport so that all documents can be verified, etc.