At a very personal level, I do think there is, during pregnancy, labour and the immediate post-partum period, a particular role for women. There is, in my experience, a bond around women who have given birth in which their own experiences are remembered, and examined at a profound level. Just as some women find the support& friendship of ante-natal classes deeply helpful, others do not wish to be part of it. My own feeling is that you should do what works for you, and your family.
Of course, most of the grandparent role, especially after the first few weeks, is not really gender related, although I do agree about the mysteries of car seats!