What appeared and spread just as the United States was acquiring and establishing its control over the far west and its native people

The answer is 'Railroads'

The Industrial Revolution in England lead to the development of trains and fast travel.

The United States quickly adopted the technology and brought in English businessmen and engineers to develop railroads in it's sprawling western states.

Railroads were integral in the early years in to cement newly acquired states under the control of the Federal government.