First, with regards to giving your army commander fighting troops or keeping him alone IMHO depends mostly on which and how many good corps commanders you have.
The issue on the one side is that with regards to MTSG (March to The Sound of Guns, corps coming to each other's aid) Lee as army commander has an advantage in MTSG'ing. He will do it more often than a corps.
TIP: Whatever you do, if you have a line of corps 3 wide, you will want to have Lee in the middle, so that he can MTSG in both directions. If you corps line is being attack on both ends (nobody is really dumb enough to attack in the middle, because both end corps could MTSG to the middle corps, but on the end, only the middle corps can MTSG to the end corps) Lee will MTSG first to one side, and then to the other.
Assuming Lee is in the middle of a 3 corps battle line and both ends of the line are being attack the same turn, if Lee's stack doubling as a corps stack, after the first battle, if his divisions have lost substantial cohesion, it will lessen the chances of Lee actually MTSG'ing to assist in the second battle. If Lee is alone, he will most likely succeed, as Lee himself cannot lose cohesion, so his chances are always the same, very good.
On the other hand, not having Lee in the middle corps stack will comparatively lessen that corps' chances of MTSG'ing to both battles, although, unless the terrain is very poor and/or the weather is bad (mud etc.) it is more likely than not that the middle corps will MTSG, at the very least once.
Now, if you only have 2 good corps commanders, the answer is simple, give Lee a corps, because it eliminates the need for the third corps commander.
You said you have two armies in Virginia. Why? They cannot fight and support each other, ever; no MTSG'ing between corps/army stacks of different armies. Lee has a very large command radius (select Lee's stack and hold the <shift> key to observe it). Unless where you need to have corps is outside Lee's command radius, you should only have Lee commanding an army in Virginia. Besides, he's your very best commander and will pass on the best stats to his corps commanders. Think about this.
If you do need to have two armies, remember, you can transfer corps from one army to another. To do this, the corps being transferred must be closer to the new army command than to the old. Once this is the status, dropping corps status from said corps, and then reinstating it using the new army. It will take one turn for the new army commander's status to be passed on to his new corps.
With regards to the Old Midwest. PH is correct that taking DC will likely win the game in one fell swoop. However, that you cannot win in the Old Midwest is wrong. It's just not as quick. You will have to fight a victory on more than one battlefield, but you will also not be fighting just one huge battle.
Which is wiser depends on forces and their distribution. You need to be able to dictate where you fight, picking only fights where you have the advantage, and where you can do the most damage, not just to troops, but strategically as well. Taking Vincennes is for example not the same as taking Cairo. Vincennes is important, without a doubt, but Cairo controls the Mississippi-Ohio Confluent, which is very important. It splits the Union Brown Water Navies and allows you to decide where to fight on the rivers.
However, if you are weak in eastern Kentucky and Cincinnati compared to what the Union has on the field in that area, he had the advantage, and it will be much more difficult to take the initiative.
Winter is coming - Jon Snow aka ... okay okay no spoilers
I would be thinking of consolidating at this point. Do you have Bowling Green? can you take it quickly. If you do have it, or can take it, you might want to build a redoubt there to help secure and hold it.
YOU-SHALL-NOT-PASS!! - Gandalf the Grey
You really want to also be looking at controlling the Ohio River as well. Is that possible? Do you have enough ironclads and gunboats (cottonclads have the best bang-for-bucks for fighting, but are limited in numbers).
To prevent the Union from crossing a major river at any specific river region, you need a fleet of 4 combat elements (generally 2 gunboat units) unopposed in said river region. They should be in DP (Defensive Posture) to reduce cohesion loss especially in winter when weather will wreak havoc on them, as it is inconsequential to blocking a river crossing. Also give each a transport if possible, so that they do not have to leave station every couple of turns to pick up supplies. The transports are optional. You can also just invest in gunboats and cycle them in and out of friendly harbors to pick up supplies and recover cohesion. Either way, a lot of micro-management is required.
If you can line the Ohio with a multitude of such mini-fleets, one in each river region where you expect the Union to attempt to cross, they will be blocked from crossing the river. And not only land stacks are blocked, but there is also a 90% chance in every supply distribution phase (three per turn, at the start of every turn, before any troop movement takes place) of blocking all supply from crossing the river at that point.
However, they can of course attack your blockade of mini-fleets, which is where your ironclads come into play. They are the anchors at the ends of your blockade line.
The issues you have with this are tricky. The fleets must be in OP (Offensive Posture) to attack an enemy fleet entering their river region, otherwise the enemy, if also in DP will simply sail right through. This is their greatest advantage. If your ironclad fleet at the end of your blockade line is in OP it will lose cohesion after a few turns, while the Union can decide when to set sail, and leave his fleet in DP (reduces cohesion loss while sailing) and simply depend you your fleet being in OP to start a fight. Under these circumstances, he can sail his ironclad fleet right past yours. Once at the the point of the river where he wants to cross you blocking will be negated. The next turn he will be able to cross the river where his ironclads are resting. He cannot plan a crossing before this, at least human players cannot, because the game engine does not allow plotting a move across a blocked river region. I'm not sure if it does allow the AI to plot such a move; IIRC it does .
The other option is to station your ironclad fleet in an harbor where it can sortee out quickly to attack his fleet once he has passed. If he sent his IC fleet in in OP he will only attack your end fleet(s). I don't recall, if after the first battle, he will continue, but I believe it depends on his fleets status after the first battle. It might continue on until being worn down.
And there is another issue you have to consider. Jon Snow, eh... winter Starting a few regions west of Cincinnati, you can expect the river to freeze. From Cincinnati and further up river, you can practically be certain of it. When a river region freezes in winter, any fleets in that region will be automatically sent into the closest friendly harbor, where they will be locked in place until the river thaws again.
This means the river can be crossed where frozen, unhindered by blocking gunboats. It also means IT'S WINTER! Moving across the land will be costly; much higher cohesion loss, much higher supply usage (some cohesion loss will be traded for supplies (the troops are getting warm gear, being fed warm food more often, etc.), and they can and will take hits. This is why we never conduct operations in winter weather if at all avoidable. If such a force spends more than a couple of turns marching through such bad winter weather, wherever they arrive, they will be in poor condition, which makes any attacks they might conduct likely to fail, which means much more cohesion loss, many hits, and likely leave them in huddled masses, practically unable to move, starving, and freezing, and ripe to be counter attacked and being wiped out. Athena is not likely to attack in winter, unless it is very close by, and victory is certain.
What you do will depend on assessing the situation and your abilities to leverage every advantage you can muster.
As PH loves to quote, "Nicht Kleckern sondern Klotzen!" (Don't slap their face, kick them in the balls!! ) - Heinz "Steel-Toes" Guderian