Comment by bell-cot
Back in the day, my middle-class American family's default was that the maternal grandmother moved in for the first 2 weeks postpartum, and the paternal grandmother moved in for the second 2 weeks. There could be quite a bit of family support above or beyond that, if needed.
As mom described it, the right mentality was not "grandma is here to take charge", but "grandma is temporary help, in your home, and stepping back from things every day as you recover".