Given the holiday weekend, and knowing that normal traffic on a Friday NB from Manhattan is terrible enough to make you cry, the nanny would have to have been really quick about going straight from school to granny's and then immediately back to CT. It's a little over an hour with no traffic, but can easily take 2 when traffic starts to back up. So the fact that it may have been pre-planned makes a lot of sense to me.
If mom had a 1p appointment in Manhattan, it's unlikely she planned to get the kids. That would have been cutting it really close. So if mom was a no-show at pickup, then the granny was called, then they found the nanny, she got to the school and took the kids, that would eat up precious time we know she didn't have since we know she was back in NC by around 7pm.