This choice had little to do with uniting the party. It was more about convenience and safety in a guy with executive experience, a long time of military service and name recognition. How differently the world might be today had Reagan not wasted his time with Ford and made the right choice with Jack Kemp.
You’re right about him offering Ford first. But Reagan did not want Ford. He thought he needed Ford. But Ford wanted to be more than a normal VP. He wanted a co-Presidency and Reagan refused. He went to the next logical choice Bush. And what I described is what happened next. The establishment did not foist Bush on Reagan. He just recognized that it was the best move politically.