No, being able to move back with your parents would not violate the 1st criteria (permanent place of abode) for NY's military Group A exceptions. Since it was your parents' home, they would be the ones maintaining a permanent place of abode
The term "maintaining" implies occupying the residence and providing for both its upkeep and utilities. Unless you (or your spouse) occupied the home and paid the costs of maintaining it, you would not have been considered as maintaining a permanent place of abode in New York State
From Publication 361 New York State Income Tax Information for Military Personnel and Veterans:
"In general, a permanent place of abode is a residence (a building or structure where a person can live) that you (emphasis added) permanently maintain, whether you own it or not, that is suitable for year-round use, and usually includes a residence your spouse owns or leases.
