I don't know that I will have this situation, but I was wondering what people's opinions are on it. I already have my own opinion.
Say you invite Mr. and Mrs. X and not their children, to your wedding, and Mr. and Mrs. X have an infant. Is it appropriate to bring the infant with them? It isn't like they would take up a seat or cost a plate. And what if Mrs. X is breastfeeding? Would a couple be expected to either not attend a function or leave a breastfeeding newborn with a babysitter?
I was thinking back to when my youngest sister was less than a month old and my mother took her to the Nutcracker at a local theater. They wanted her to pay for a seat for the baby! My mother had only assumed that it wouldn't be an issue since the baby was literally like three weeks old and not bottle feeding.
I would expect this person to bring the infant with them. I would also expect that they would leave with the infant if they are crying.