My sim gave birth to triplets .. when she already had a toddler and an infant. When the triplets aged up to infant, since their mother can only do tummy time with one at a time, I hired a Nanny. But ...
Ideas
I unfortunately don't think this is a bug, as I've never seen this be an option, but even if it's deemed "as designed" hopefully the Sims team will change it, because yes, nannies should absolutely be available for ALL infant tasks.