I don't feel like kaname had children with the hooded woman either. Hino's story is just inconsistent and full of plotholes
She really did just make the story up as she went along. First depression because Kaname's lover died but nope, Kaname went into a sleep actually because he saw Yuuki. Bruh, which is it? All an author can do is hope that things make sense as they make it up and not leave too many plotholes to sink into their story.
Someone pointed out that Juuri and Yuuki can both use anti vampire weapons being the natural born descendents of the mother metal, and that does kind of make sense to me. Now IDK about Juuri’s case specifically, but I always read Yuuki being able to use them as a form of the hooded woman 'accepting her' as Kaname's/humanity's protector. I think both of their warm feelings they had towards humans may have been what got acceptance from the heart of these weapons (that woman who sac'd herself for humanity.)