If Lee is replacing McClellan he'd be doing so after First Manassas (McDowell was in command then and took the blame). Let's say his corp performs better than the rest of the AOTP, making some last minute charges to delay the Confederate pursuit.
I find it quite unlikely that there would be a 1st Manassas because Lee was alway a Virginian first and an American/Confederate second. So if Lee is in command of the premier Union Army we must assume that Virginia never left the Union.
The Army of the Patomac (Union) is unlikely to exist either.
But for the purposs of answering the rest of you post I shall ignore plausability and go with the idea that Lee's remained in the Union while Virginia left.
Afterwards we have a very real POD. What would Lee do? I doubt he'd think of something as novel as an amphibious landing on the York-James Peninsula as in OTL. Plus lets not forget he was constantly offensive strategically and tactically minded (as long as he had enough men and supplies) and constantly let his prey escape by delaying at the worst time (Chancellorsville, 7 days, 2nd Manassas). These are two major problems especially against a defensive Johnston (who turned northern Georgia into hell for Sherman) and a land as easily defendable as northern Virginia. 1862 may be the year of stalemate for Lee.
However Johnston won't last long in Virginia. His relationship with Jeff Davis was deteriorating rapidly and neither wanted to be near the either. Who would replace Johnston? Jackson? Longstreet?
Joe Johnston's main problem is Jefferson Davis. Davis holds no stock in a defensive war he wants an offensive-defensive one. Joe Johnston however works on the principle that it is better to lure you enemy to a battlefield where you have the advantage and can overwealm your enemy with a powerful counter-attack than it is to charge after them and fight them on whichever battlefield you find.
I can see Joe Johnston being quite sucessful against Lee but not being able to destroy his enemy and so the Confederate President is likely to remove him.
On the issue of who would replace him I'm afraid that there are only two possible choices, Beauregard or Bragg. A.S.Johnston would be Davis' first choice but he would be either occupied in the West or dead and Bragg was a man who Davis held high hopes for as an Army commander while Beauregard is generally on bad terms with Davis.
Jackson and Longstreet wont be though of highly enough to be considered as it unlikely that either of them will have estabished themselves as ANV commander material.
There is an outside chance for Edmund Kirby Smith or John Bankhead Magruder to get command but their chances are very slim.
Jackson was also aggressive tactically and strategically but showed at Second Manassas that he was also an expert at the initial defence then counterstrike. Also unlike Lee, Jackson always seemed to know the right time to strike (again at 2nd Manassas Jackson urged Lee to attack on the morning of the third day when the AOTP was weak...Lee delayed until 4pm with only over an hour of daylight to go)
I have no doubt Jackson would've taken the war over the Potomac as he always craved too. Lee would meet him before he reaches Washington and the result would be like fire and ice. Would Jackson perform a Second Manassas and Lee a Malvern Hill? Or would Jackson be sucked into a Fredericksburg?
My guesses are that Jackson is no fool and would choose the ground that Lee would meet him on (as Longstreet insisted at Gettysburg). Lee would go into his Gettysburg/7days mode (he is here therefore I havta whup him here) and be drawn into a trap (Jackson always carefully chose his ground, making sure there was enough of an advantage to make a flanking attack).
One thing you seem to be overlooking. No matter how great a battle-field commander Jackson was (and he quite possibly was the greatest in American history) he had little to no organisation skills, and cirtainly he had no ability to communicate strategies with men under his command.
What Lee doesn't seem to get enough credit for is his re-organisation of the ANV after the 7 day battle. Becuase when Lee took command of the ANV the units of the Confederacies premier army were still split by state and were not a cohesive army but Lee used the 7 days to work out the abilities of his commanders and kept the ones he needed and got rid of the ones he didn't During this time he also re-organised the army into a different structure of the two wings we know as Longstreet and Jacksons Corps.
What Lee also did before he became commander of the ANV was to prepare the Richmond defences and crucially he managed to seccur the men under Ewell to be sent for Jackson's use in the Valley campaign, a move that quite possibly gave Jackson the manpower needeed to win that campaign.
Lee may not have been as good a battlefield commander as Jackson but he was a much better organiser and he gave men under his command a bit more freedom which prepared them for their own commands while Jackson did everything himself which left his corps without suitable leaders after his death.
If Longstreet is put in charge instead I don't think Lee'd stand a chance, he was too much in the old school while Longstreet understood the advantages of a good defensive line. Again in my opinion Lee would be drawn constantly into a bad attacking position and would probably be replaced by a more creative commander. I'm not anti-Lee or anything its just the impression I've gathered of his mental abilities and attitude after reading several dozen books of the ACW.
Except when Longstreet was given individual commands (however small a chance that was) in the OTL he showed considerable lack of immagination (the seige of Suffolk, Battle of Campbell's Station and the battle of Fort Sanders) so it is not fair to assume that Longstreet would be too good for Lee to defeat, especially if they clashed early on before Longstreet had a chance to hone his skills.
Plus what you have to remember is that without Lee, Longstreet would not have gained the positions of power he did in the OTL...at least as early. The main reason for this is that wihtout Lee's reorganisation Longstreet and his forces would still be part of the badly organised ANV and would likely be given few opportunities to excell.
On the subject of Lee's Army of the Patomac I have always wondered as to whom he would choose as his suboordinates. The main one if the obvious choice of George Henry Thomas because Lee knew him well as a soldier and knew what he was capable of but that still leave at least one other commander for Lee to pick. I have no idea who that would be.
However with George Henry Thomas and Robert E. Lee in one army against the Confederates no commander is just going to be able to defeat the AOTP with ease.