You do know that mythology is all dependent on the time period of which you quote it from right?
Yeah. Though the problem with using the "real life lore" argument is that there really isn't any such thing. What we have are thousands of years of stories which all say different things... some of which are completely made up, and others are based on historical figures who do not have the kind of mythological powers the stories would suggest (eg, if you look into the basis of the Dracula stories expecting to find a real person who could turn into a bat and could only be killed by a stake through the heart, you'll be sorely disappointed). There's nothing you can point to and objectively say "this is what it's like in real life lore". You can point to one thing, and I can point to another with the same veracity.
Though I do must apologize for my ranting. It's a reflex when I see something pointed as 'almost always true elsewhere' that's only somewhat true in pop culture. But saying "lore always states vampires and werewolf hate each other, in most all movies, books and games even including real life mythology about them," is simply not true. Most all movies, books, games, and real-life mythology do not have werewolves and vampires hating each other for what they are. Most of them that have vampires or werewolves don't include both creatures, and of those that do, not all have them at war.
I also never stated that TES follows anything. I said that it is typical of most movies, games and books to have werewolves at the throats of vampires and vice versa so whats not to say that Bethesda wasn't trying to do that with the Silver Hand which is highly supported by the fact that most of them drop vampire dust when they are killed which would follow modern day movies and books.
Because TES lore does not follow that formula. There's nothing in the games to suggest the two creatures have a particular hatred for each other*, and there's no reason to think they should given their creation and purpose. Really, the only thing werewolves tend to hate are themselves (as they have no control over themselves in beast form, yet can remember all the killing and eating they do; it drives them insane and often causes them to lose their minds).
* There is a small instance in Daggerfall where a vampire states they prefer drinking werewolf blood because it tastes better, but that's pretty much it. Vampires still most often go for the blood of regular people, not werewolves. There's no grand-scale attack against werewolves by vampires, or vice-versa.
They carry vampire dust for the same reason they carry mudcrab chitin and hawk feathers.
IIRC, they don't have Vampire Dust on them before they're killed. I'll again lament that Bethesda didn't make all vampires turn to ash when killed, and instead opted to just add Vampire Dust to their inventory on death. Maybe I'll run through a Silver Hand hideout with Dawnbreaker and see what happens (now that vampires are properly treated as undead, finally).