For Moe et al., let us consider the legal status of the Corps commanders. I'll do this chronologically.
Firstly, the original five corps were created by Presidential fiat. There was no legal basis for the existence of corps, and hence no way for them to claim for staff etc., who had to be seconded from the infantry divisions. I believe in most cases the promoted corps commander took his divisional staff up as the corps staff. Lincoln's
War Order No. 2 names their commanders.
In late April Hamilton is relieved by McClellan at Heintzelman's request. They would have been within their rights to arrest him, but they spare him (and Lincoln) the embarrassment. Lincoln asks McClellan if he could reinstate Hamilton, and McClellan replies only if Lincoln orders it. Hamilton will go west and eventually be fired by Grant.
Soon after, Williamsburg is fought. Given the poor performance of Sumner, Heintzelman and Keyes McClellan sends the following which deserves to be quoted in full:
"I respectfully ask permission to reorganize the army corps. I am not willing to be held responsible for the present arrangement, experience having proved it to be very bad, and it having very nearly resulted in a most disastrous defeat. I wish either to return to the organization by division or else be authorized to relieve incompetent commanders of the army corps. Had I been one-half hour later on the field on the 5th we would have been routed and would have lost everything. Notwithstanding my positive orders I was informed of nothing that had occurred, and I went to the field of battle myself upon unofficial information that my presence was needed to avoid defeat. I found there the utmost confusion and incompetency, the utmost discouragement on the part of the men. At least a thousand lives were really sacrificed by the organization into corps.
I have too much regard for the lives of my comrades and too deep an interest in the success of our cause to hesitate for a moment. I learn that you are equally in earnest, and
I therefore again request full and complete authority to relieve from duty with this army commanders of corps or divisions who prove themselves incompetent."
It is important to note that McClellan is requesting authority to relieve Sumner etc. This immediately demonstrates that he does not have said authority. This should be obvious; Lincoln has ordered them to be Corps Commanders, and no general can countermand the order of POTUS (or SECWAR wielding the power of POTUS).
The reply was in two parts, a telegram and a handwritten letter. The telegram read:
"
The President is unwilling to have the Army corps organization broken up; but also unwilling that the commanding General shall be trammelled, and embarrassed, in actual skirmishing collision with the enemy, and on the eve of an expected great battle; you therefore may temporarily suspend that organization, in the Army now under your immediate command, and adopt any you see fit until further orders. He also writes you privately."
and the letter:
"I have just assisted the Secretary of War in framing the part of a despatch to you, relating to Army Corps, which despatch of course will have reached you long before this will. I wish to say a few words to you privately on this subject. I ordered the Army Corps organization not only on the unanimous opinion of the twelve Generals whom you had selected and assigned as Generals of Division, but also on the unanimous opinion of every military man I could get an opinion from, and every modern military book, yourself only expected. Of course, I did not, on my own judgment, pretend to understand the subject. I now think it indispensable for you to know how your struggle against it is received in quarters which we cannot entirely disregard. It is looked upon as merely an effort to pamper one or two pets, and to persecute and degrade their supposed rivals. I have had no word from Sumner, Heintzelman, or Keyes. The commanders of these Corps are of course the three highest officers with you, but I am constantly told that you consult and communicate with nobody but General Fitz John Porter, and perhaps General Franklin. I do not say these complaints are true or just; but at all events it is proper you should know of their existence.
Do the Commanders of Corps disobey your orders in any thing?
When you relieved General Hamilton of his command the other day, you thereby lost the confidence of at least one of your best friends in the Senate. And here let me say, not as applicable to you personally, that Senators and Representatives speak of me in their places as they please, without question; and that officers of the army must cease addressing insulting letters to them for taking no greater liberty with them.
But, to return,
are you strong enough-are you strong enough, even with my help-to set your foot upon the necks of Sumner, Heintzelman, and Keyes all at once? This is a practical and very serious question for you.
The success of your army and the cause of the country are the same; and of course I only desire the good of the cause.
Yours truly. A. LINCOLN."
What is clear from this is that McClellan's request to be allowed to relieve the three corps commanders is denied. Lincoln and Stanton however allow him to temporarily modify the structure. Hence McClellan creates 5th and 6th Provisional Corps. Provisional as Lincoln has not authorised them, McClellan has.
Just to be clear moving forward; Lincoln and Stanton have confirmed that McClellan is not allowed to relieve a Presidentally appointed Corps Commander. Incompetence is not considered an adequate reason.
On 2nd July 1862 the House passes Resolution 51, which authorises the President to form Army Corps, and allows for Army Corps to have staff assigned. It is signed into law on 17th July. On the 19th McClellan asks that the President ratify Porter's 5th and Franklin's 6th Corps. He does this and also
orders the forces at Ft Monroe under Dix to constitute 7th Corps, those at Baltimore under Wool to constitute 8th Corps, and those under Burnside to constitute 9th Corps.
Going into the Maryland Campaign, four of the corps commanders are Presidential appointees (Sumner, Porter, Franklin and Burnside). As was confirmed on 9th May, McClellan does not have the power to relieve them. Doing so would be a violation of Lincoln's orders making them Corps Commanders.
So, McClellan can't just relieve Burnside like he did Hamilton. He has to arrest him. This is extremely serious, as disobeying orders is a capital offense. In theory Burnside could hang. If he doesn't hang then if found guilty he'll be drummed out the service and barred from serving the government in any capacity (i.e. what happened to Porter). With such a serious crime, the evidential standards are high. McClellan has to deliver a written, peremptory, lawful order and Burnside then has to refuse to obey the order. At 1000 the only written orders we know of are for Burnside to "open your attack".
Hence the only way to remove Burnside is to issue a written, peremptory, lawful order, and then arrest him if he refuses to obey it. It seems this is what Key carried (it is certainly true of 29th June). However, by this time Burnside is over the bridge, and hence the order is superfluous.