Thank you for sharing. Since the beginning of this case I've thought about Katie Holmes (Tom Cruises). She had a complete apartment set up with armed guards when she was able to leave him. Yes, I believe moving to NC was a safety plan, just not sure why she lacked security for her own safety.
JMOO... I don't think JD would have time to change clothes, after dropping the kids off and catch a train or drive to an appointment in NYC. I think the appointments were local, mainly due to LE timeline.
MMO, I think when the nanny was unable to reach JD she took the kids to NY as a prearranged plan. The "visit to Grandma's" was just part of the prearranged "story". I'm sure everyone lived on pins and needles.