I agree.
But, the Empire is the utmost logical choice to ensure the survival of mankind, and the utter destruction of the Dominion.
Not always, and it all depends how we look at something in lore. To illustrate my point, I'll attack your argument (I am sorry!).
The Stormcloaks are fighting one Legion. They are fighting the 4th Imperial Legion sent by the Empire to quell the rebellion.
The Fourth Legion has never been mentioned in Elder Scrolls Lore (That was a mistake done one wiki and it spread like the plague.)
Since all other Legions are on the front lines near Valenwood and Elswyr, they cannot send reinforcements.
Imperial soldiers are escorting barrels of mead.
Lady Maven Black-Briar,
I've made inquiries into the loss of your mead shipment to Cyrodiil, and I've come to the conclusion that they were waylaid by a group of mercenaries under the employ of the Empire. According to my sources, these mercenaries were not acting under orders and simply attacked the caravan for supplies. I've forwarded a request for compensation on your behalf to the Imperial Council and the mercenaries in question have already been dealt with accordingly. Again, I wish to extend my deepest apologies for this unfortunate mishap and I assure you that any future shipments into our nation will be met at the border by an Imperial patrol and personally escorted to its final destination.
Reginn Limilus
Grand Steward, Imperial City Trade Relations http://www.uesp.net/wiki/Skyrim:Regarding_Your_Loss
Thus explaining why the 4th Legion, ONE LEGION, is weakened. Even before and after Whiterun, Galmar states to Ulfric that their "men are being slaughtered out there." I can find this quote for you if you wish.
"That's what comes of trying to win a war with a bare handful of legions. If the Emperor would just give me the reinforcements I've requested!" - General Tullius http://cs.uesp.net/index.php?game=sr&formid=0x000d767b
The Empire is having trouble because all other 17 Legions are being rebuilt and are being stationed in the south of Cyrodiil in preparation of the next Great War.
The problem with this is that the Empire was mentioned to be militarily weak prior to the outbreak of the Great War. Having also lost Legions during the Umbriel Crisis around 4E 40, the highest Legion mentioned in the Great War is the Tenth Legion.
Had the Empire placed every single one of it's Legions in Cyrodiil they would begin to lose the outer regions as seen during the Great War and a bit after as the Kingdom of Wayrest was lost to pirates.
This forces the Legion you're fighting in Skyrim to recruit locally as the Empire cannot afford to send reinforcements. Plus, you keep mentioning that the Empire can't quell this supposed "chaos" in Cyrodiil? Quote where this is stated as I have never heard this before in-game.
The situation in Bravil grows more dire. The city has erupted in violence, due to a war of control being waged by Cyrodiil's two largest skooma traffickers. The Listener, Alisanne Dupre, has been forced to employ sellswords to protect her own residence.
Being forced to recruit mercenaries for protection, indicates the Legion does not have control of the situation (This is 13 years after the Great War).
Cheydinhal has erupted into violence and chaos, like so many other cities before it.
Another city starting to fall into problems (This is 14 years after White-Gold Concordat). It is not mentioned if order is restored although there appears to still be some issues only one year prior to Skyrim starting.
Bruma is also another city that erupted into violence.
The Empire won't trade with a providence that just kicked its ass out of it's own territory. Plus, it is heavily evident both in-game and out that the Empire and Skyrim hold a very strong, and prosperous trading bond. Once with is broken, then what? The Empire will be further weakened from this, and so won't Skyrim.
They're willing to possibly accept trade deals with the Aldmeri Dominion.
"A delicate question, to be sure. I'm the Emperor's cousin, and the Empire has little love for the Thalmor. On the other hand, the Thalmor have considerable funds and are looking to expand their shipping. I haven't signed any deals yet, but I'm sure my cousin will want a cut if I do. What better way to soothe his wounded pride?"
You really believe an Independent yet weak Skyrim can live off of it's own resources, and have such an endurance to survive an Imperial invasions.. AND be able to fight the Dominion. I highly believe otherwise.
Skyrim is quite robust, they have alright farmlands in the Rift and plenty of fishing and game to hunt. They trade with Morrowind and even Hammerfell, there is a Nord shipping company in Windhelm that is in fact doing extremely well (enough to force the EETC into no longer sending ships and the warehouse in Solitude seeing little use apparently for a time.)
The Empire uses the "Septim" as their currency. All territories of the Empire use this currency. If Skyrim is severed from the Empire, the Septims will be rendered useless as it is an Imperial currency. That's like saying America keeping the British currency after winning the Revolutionary War is logical. That makes no sense. Just as what happens to any new nation, Skyrim will have to set up a new economic system and government. This will lead to inflation issues, trade conflicts, etc.
The gold coin, septim and drakes are all interchangable. Silver is also an acceptable trade, as both the Stormcloaks and Empire use it.
Sorry to burst yet another bubble, but the marriage of an Imperial with a Stormcloak would only cause more unrest. Just because some pompous and naive Imperial from Cyrodiil says that things will be A-OKAY with the new marriage doesn't truly represent anything. The Stormcloaks would still hate the Imperials as they want their land free from the Empire, marriage of an Imperial or not.
Marrying into royalty is actually a common political move, and First Cousin to the Emperor is pretty well placed. Wouldn't be the first time the Empire and Skyrim solved political problems through royal marriage.
It wouldn't exactly create peace instantly, but it could have been steps towards it.
The Emperor arrived in Skyrim because his own family was killed. Thalmor battlemages are there thanks to Ulfric and his Rebellion. Uh, there is no heavy presence of Imperial ships in Skyrim besides the ones of the Empire Trading Company. And you still lack the understanding that the Legion lost 60 percent of it's forces. It's going to take a bit of time to rebuild an entire army..
The Emperor arrives to become directly involved in dealing with the rebellion. Hence why it is mentioned his hand is forced as Titus II was unwilling to become directly involved in the conflict (cancelling his original trip months ago).
There is one Imperial vessel I know of (Believe you cause it to shipwreck in a quest involving an Argonian). It carries pay for soldiers and weapons.