In the Official Guide is written, to track the schedule of the sim that goes to work *earlier*, to make sure that the nanny comes early, and if she doesn't come - the second sim has the time to call her "just for now", and at the end of the working day - to make a new "track schedule".
Actually, that's not quite what the guide says. Page 212 of the guide says "If parents work differing hours, consider having the earlier-departing adult call the Nanny. Thus, the later-starting adult can work on Skills or Wants or socialize rather than taking care of the minors."
The guide doesn't say anything like "if the nanny doesn't turn up then you can use the other parent to call the nanny" - I would have been surprised if it did, as that's effectively saying this is bugged so this is the workaround. Remember that the guide was written before the game was released and therefore before the bugs in the released version were known.
Yes, I did buy the guide for the original game, before I realised that the guide is basically garbage.