First Aid box Yes. But the most important tools for an emergency backseat, house or roadside delivery is a sterile razor blade or pair of scissors and two pieces of clean strings (uzi) each about 20 cm.
The most important skills are knowing where to tie the two strings along the umbilical cord and where to cut. Of course how to hold the kid and how to initiate crying if the baby comes out too shocked to cry.
For warmth, women always donate their lessos or your jacket/sweater could do. Then next stop must be hospital even if all looks okay.
Unfortunately, gone are the days when every woman's purse has a leso. My mum carried one everyday everywhere.