Is ptosis genetic and could I pass it on to my children if I have it?

Congratulations on your pregnancy. What we mean is that it was either present at birth or in early childhood. If you told me that all the cousins also had ptosis, then it would much more likely it was a "genetic" ptosis. I have seen identical twins where one had "congenital" ptosis and the other no ptosis. So I would fret over this too much.