I carry more than that when I’m taking a trip to the range.
Was it illegal in her state at the time to have that in her car?
No, as long as the shotgun/”assault rife” were unloaded and in locked case or compartment out of reach of the occupants of the vehicle and the ammo is stored separately from the firearm or in a locked container. So-called assault rifes have been illegla in NY since at least the 1990s.
Note that if her firearms were illegal at the time of arrest, then she would have also been charged with a firearms related crime, rather than simple trespass and she would not have won her false arrest suit.