So I've been trying to figure out how magic is passed down, because if it's only passed down from mother to child, then Harry shouldn't have magic, and I think I've come up with something:
There are two parts to inheriting the ability to use magic: genetics and exposure to magic in the womb.
You can get the genetic component from either parent.
You also need to be exposed to some degree of magic while in the womb. This is significantly easier if your mother is a magic user, because there is always some magic circulating through magic users even when they're not casting spells (based on the fact that wizards still hex things even when not using magic).
It's significantly harder to be sufficiently exposed to magic if your mother is not a magic user, because it requires that your mother be around multiple fairly powerful magic workings while pregnant with you. This explains why magic appears to normally be inherited from the mother, especially with minor practitioners.
This also explains why Molly inherited magic from Charity but none of her other siblings did: Charity wasn't practicing magic while pregnant with her, but she hadn't stopped long enough for magic to stop circulating through her yet. (After all, if it were just genetic, then Charity abandoning magic would have no effect).
It also explains Margaret--her mom wasn't magic, but was hanging around Ebenezer (since she was married to him).
In addition, it explains both why Maggie might have magic and why it would be influenced by her mother's vampirism--she inherited strong magical genetics from Harry, and was exposed to rampire energies rather than mortal magic while in the womb.