I can answer part of your questions. The four brothers are undoubtedly the four half-brothers of my great grandfather George TerBush.They were born in New York State from 1820 to 1834.All moved to Michigan, where they appear on the census as T.Bush, and at least some of them appear later as simply Bush.
Their names were Jonathan (oldest), William, Osband and Albert L. (youngest)The three oldest all settled in the Grass Lake area of Jackson County.
They and some of their offspring are covered on pages 45-47 of "The Descendants of Jan Bosch (ter Bosch)(16__-1678) of Germany, Holland & New York City", published by my sister and I in 2001.
Bush is such a common name that we didn't make a great effort to follow those branches who dropped the "Ter".However, since publishing the book, we have been contacted by at least two of their descendants, who provided us with much more extensive iformation on them.
I am not sure of the history of your Daniel Bush.There was a William L. TerBush who moved from New York State to Ingham County, MI, then later settled in Clare, Clare Co., and still later had a farm in Isabella County.However, he was born in 1833, which would make him much too young to be the father of your Daniel.Also, his descendants seem all to have maintained the Ter, and neither of his wives had names close to that you show for the mother of your Daniel.
I was born and raised in Tuscola County Michigan, but now live in Alexandria, VA.