Could a VampireWerewolf hybrid exist based on Stephenie Meyer's Twilight world?

No because, according to "breaking dawn" when a vampire bites a human they are transformed but when a vampire bites a werewolf its like poison. So they could never form a 'child (creature) without killing itself though poison.

But also, Jacob and his gang aren't actually werewolves, as described in "breaking dawn" Real werewolves are called "children of the moon" which are children who transform into werewolf savages every full moon. Jacob and his gang are simply shape shifters who have taken the shape of a giant wolf (unrecognizably chosen by the Quillete people centuries ago)