Which universe is the alternate one again?
In Storm Front, part two, Daniels said this: The timeline's resetting itself .... all of the damage he caused, it never happened
From that I get that basically the first two seasons of ST: Enterprise existed in an alternate universe. What the NX-01 did originally in the prime universe is difficult to say. But whatever it was, it would have been at least somewhat different than the events depicted on the show.
The first two season are not a part of the history of the other series, any more than the events of In A Mirror Darkly.
That doesn't hold up at all. Daniels was referring to the damage Vosk and the other factions did when did when the TCW went nuclear, creating the alt-WWII timeline.
Events from seasons 1-3 are repeatedly referenced in season 4. The Enterprise crew lived it, and other characters like Captain Hernandez and Soval and especially Shran were familiar with those events. Some of the stories, like the Vulcan reformation arc and the Vulcan/Andorian war, were continuations of previous stories.
I really don't see the need to explain real-life story retcons (i.e. rewriting Klingon/human first contact, ignoring parts of "Balance of Terror") in an in-universe perspective, let alone in a way that makes Enterprise, or part of it at least, essentially all a dream.