Yes.
Your narrative on this question is extremely McClellan centric, which is seeming to cloud your judgement. The simple fact is that in this expanded war Lincoln has made decisions that certain strategic areas and the generals be ****ed. McClellan is just another general, who serves as the president's pleasure. Stanton has been making far sighted decisions for saving the capital, providing for a continuation of government, and the overall defence of the nation. McClellan is only defending the Virginia front, and there are many others to be concerned with. Lincoln has decided any general in the army is disposable for the defence of Washington, Stanton used that power to detain both Porter and Franklin.
But again, McClellan may not presume to know Lincoln's mind better than Stanton. He may demand an appeal to the President after the fact, but that's it.
Okay, so, to be clear, Lincoln has decided that it's okay for Stanton to get rid of McClellan (who is the General in Chief), but he isn't providing a signed order to that effect because
It's just that McClellan historically had the confidence of Lincoln until November 1862. Here, despite what some call a lackluster performance, he's driven the rebels away from Washington, followed up with an attack into Virginia, and deterred any major invasions of the North by Johnston or Lee at First and Second Manassas Junction, then with the stalemate at Culpeper. Lincoln has no reason to assume he's incompetent or unwilling to follow orders.
So Lincoln has enough confidence in McClellan to not want to get rid of him, but he also has insufficient confidence in McClellan to give a major political foe of his the ability to remove him unilaterally.
I think this is a bit of a contradiction going on. It's not as if there are unlimited numbers of high ranking generals, and if I understand correctly McClellan is one of only a few at most who was appointed to his position
by the President personally (as opposed to by the authority of the commanding general etc.), so it's not as if McClellan is "just" another general - he's the highest ranking uniformed officer in the country, and it is absolutely a matter for the President's consideration whether that man has his confidence or not.
Either (A) Lincoln delegated authority to Stanton on the understanding that it meant McClellan (specifically) was going to get zapped by his enemy Stanton as soon as Stanton felt like it,
Or (B) Lincoln does not think it's appropriate to get rid of McClellan (and thus would either not delegate that authority to Stanton or would delegate the authority but exempt McClellan from it)
Or (C) Lincoln didn't even think of it as a possibility and it didn't enter his consideration at all.
If (A) obtains then there is no reason for Lincoln to not provide a signed order providing for the relief of the General Commanding.
If (B) obtains then Stanton has no authority to do this.
If (C) obtains then Lincoln didn't even think about whether his highest ranking uniformed officer should keep his job or not, which means Lincoln is terrible at politics.
I think that if what you want is for McClellan to be relieved of command then (A) is the option you should go with*, but you have indicated that Lincoln is actually supporting McClellan on the whole and thinks he's doing a good job. Which means the only possibility for this situation to come about in the first place is (C).
* such as, for example, having Lincoln provide Stanton with a signed order which Stanton then uses, which cuts through any of the ambiguity and is a reasonable course of action for Lincoln to take - it'd be ten minutes of contingency planning at the outside.
The cause of this "legal deadlock" is that you've assigned Stanton powers Stanton
did not possess at this point historically, because if he had them he'd have got rid of McClellan off his own bat. Instead when Stanton wants to do things like "assign troops away from McClellan's army" he goes
to Lincoln with an argument for why those troops should be assigned away - rather than just doing it himself. So it seems clear that Stanton
at the very least historically needed buy-in from Lincoln even to order corps and divisions around between departments...