The provinces are like strands in a twisted rope, while the Dominion are a pair of scissors. Together the rope has a much better chance of not being cut by the scissors, but if untwisted and individually cut, they don't stand a chance.
Then why doesn't the Dominion want the Stormcloaks to win the war and the province to secede? Divide and Conquer isn't their strategy, it's more like distract and disintegrate. Regardless, Skyrim would be extremely hard for the Aldmeri Dominion to conquer. If they launched a naval invasion from the north their fleet would not fare very well in the treacherous Sea of Ghosts, and to get there they would have to sail past Hammerfell. The other way into Skyrim by water is the White River, which would be a death trap. The Rift is protected by the Jeralls, and Markarth is also very mountainous. The only viable way into Skyrim is through Falkreath, and if the Dominion was invading Skyrim, I doubt Cyrodiil would stand idly by (then again, you never know with the Imperials nowadays.)
They won't have anymore success than they did with hammerfell.