@Grimmycoffee Tewi being secretly powerful is just a popular fan theory and (probably) nothing more. It really doesn't have anything to do with her myth, it's more about how the myth itself took place thousands and thousands of years ago, how her ability can manipulate luck, and how we know from Yuuka that normally weak youkai can end up insanely strong just from age.
Eirin isn't Tewi's master. They have a deal where Tewi allows them to stay on her territory, The Bamboo Forest of the Lost, and even helps them sometimes in exchange for Eirin teaching the rabbits science and medicine, and providing medical treatment for the rabbits. Outside of being an amazing doctor, Eientei actually doesn't have much political clout, in Gensokyo at least. This is mostly because they are still in hiding and are pretending to be humans and very few characters outside the playable Imperishable Night cast are even aware that they're Lunarians. Similarly to the Scarlet Devil Mansion they aren't a major faction trying to control Gensokyo behind the scenes like the Tengu, the Tanuki, Moriya Shrine, the Buddhists, the Taoists, or Hell. They're basically just seen as a bunch of suspicious, self proclaimed "humans" living in the woods.
The source for most of this info is in Silent Sinner in Blue/Cage in Lunatic Runagate, Perfect Memento in Strict Sense, and a little Bohemian Archive in Japanese Red.