Keep in mind that, because Momaday does not tell us the precise reason why he includes violence, this is ultimately a question about the reader's opinion. In my opinion, Momaday includes violence against the Kiowa tribe because it is a true part of their history.
Kiowa history is an important part of The Way to Rainy Mountain, a third of it, in fact. The reader can extrapolate this just by looking at the organization. The Way to Rainy Mountain is divided into three major parts: "The Setting Out," "The Going On," and "The Closing In." These three major parts are then divided further into twenty-four numbered sections, each having three separate voices: one mythological, one historical, and one personal. You can find the answer to your question written in the historical voice of Momaday's work.
In conclusion, keep in mind that Momaday's The Way to Rainy Mountain contains accurate historical dates and happenings found within the second of the two voices in his twenty-four sections. Momaday is not interested in lying about the Kiowa history. He is simply stating facts when he speaks in the historical voice. In short, Momaday includes violence towards the Kiowa tribe because that violence really happened and is part of the tribe's history.