My information suggests that this William Aylett was the son of Philip Aylett and Martha Dandridge. The William who married Anne Ashton and Elizabeth Eskridge was thus his uncle. Ann Aylett Washington was his cousin. I think Judith was his aunt.
As I've posted elsewhere I'm very sceptical that the Ayletts were descended from the Howards - I know lots about the UK Ayletts and have no evidence at all for that.