The First Presidency are the primary organizational leadership in the hierarchy of the church. (D&C 107: 22.) They are the presidency of the church. They set the agenda and are accountable for keeping the church running.
The Twelve are equal in authority. (D&C 107: 23-24.) They differ from the First Presidency in their responsibility. They have no authority within organized stakes, but are missionaries, whose job is to spread the missionary work throughout the world. When there is no organized stake, they preside because of their role as a “traveling high council.” But their authority to administer in a stake ends once a stake is organized.
The Seventy are equal in authority. (D&C 107: 26.) Like the Twelve, they are missionaries. They fill missionary assignments when the Twelve cannot be present.
The stake High Council forms a quorum equal in authority. (D&C 107: 37.)
Joseph Smith never called a member of the Twelve into the First Presidency. They were sent on missions. In Nauvoo, Joseph presided over the sitting High Council, as you can read in the minutes of the Nauvoo High Council.
When Brigham Young wanted Sidney Rigdon excommunicated, he recognized as a member of the Twelve he had no authority to do so. Therefore, the trial was before the Nauvoo High Council.
When Joseph died, and Hyrum predeceased him, there was no one designated to replace Joseph. D&C 43: 4 required Joseph to designate his successor. He did this. It was Hyrum. (D&C 124: 91-95.) Therefore, there was no successor.
Interestingly, Section 107 was not referred to in the succession process in August 1844. Nor was there a revelation given to settle the matter. It was handled as a political event, with an election by common consent. Brigham Young campaigned for the Twelve, not for himself. Rigdon campaigned unsuccessfully to wait for one of Joseph’s sons to be old enough to assume the role. The election in Nauvoo was primarily between those two options. In the months following however, others would make claims and would peel off followers.
Once the Twelve were elected as the replacement leadership group, they have thereafter remained in control. Today there is an oligarchy of the Twelve governing the church, and they control everything, with the senior member becoming the automatic successor President, and the First Presidency invariably organized from the Twelve (though there have been exceptions).
Although the Twelve and the Presidency of the Seventy were responsible for my excommunication, they lacked the jurisdiction to implement their decision. Therefore, it was necessary to employ the stake, which had jurisdiction, to accomplish this.
I’ve appealed to the First Presidency. But what I find interesting is that the process in my case has involved the stake high council, the Presidency of the Seventy, the Twelve, and will now also involve the First Presidency. All of those quorums which are “equal in authority” are to be affected by this decision. Only the Lord could bring about such an interesting alignment of responsibility for this decision to excommunicate someone for their belief in scripture, belief in prophecy and their historical viewing of Christ’s prophecies about us and our behavior.