This is purely speculation but I think Peter's decision to align with Carol is probably based heavily on the fact that last time he rode with Stark on a major issue like this (presumably involving the govt this time as well) his life went straight to hell so I'm guessing he's hesitant to back Tony again.
Personally I think Peter screwed himself last time by not having a spine & saying "Hell no I will not reveal my identity to the whole world!!!" but like I'm said I'm guessing he has trust issues with Stark still.