I'm beginning to think that how well a nanny does depends on their traits. I just fired one. I got a message that the baby was hungry but the nanny was focused on helping the child with piano. Great that the nanny was helping the child, but the baby hadn't been fed. Yep, fired him. He wasn't exactly lazy, but I didn't like how he multitasked.
So I hired a new nanny. Now the new nanny, she's not an elder so she can move around a bit faster and she's on top of everything. I tip her everyday too, so I don't know if that helps any. But she multitasks with all three of the kids (baby, toddler, child). To add some drama, the husband had an affair with the nanny, who is now pregnant...so not sure how that will work...if I'll get to keep her as a nanny or not. I hope so, as she's the best I've ever had in game, as far as taking care of multiple kids and being on top of everything.