Yeah, I'm reading this as "We weren't up to dealing with the husband's family's boundary-trampling until we got home from the hospital," particularly the concern that the grandparents would take it upon themselves to visit.

A long, painful, requires-months-to-heal delivery is the kind of thing where "surprise" visitors can be very unwelcome and counterproductive, and being exhausted afterward and wanting to rest and bond with your new baby is completely reasonable!

The letter may have been cut down for length, but I think it's pretty clearly implied that the reason they waited to notify the grandparents was so that they could get through the delivery/first hours of recovery without dealing with other people being physically present or aggrieved that they weren't invited.