I appreciate the passion you show, Kintachi, and I wish you good luck for your mod, which will require tons of work from the sound of it.
A few things, as R.Graves already said:
About the legion problem:
-How would the NCR be able to cross the Legion's territory? These are three States we are talking about. It's huge and filled with hostiles. Considering how difficult it is for the NCR to maintain a proper military structure within the Mojave, it would be impossible for them to do the same in enemy territory thrice as big, even if they deployed their entire military.
-Caesar's death should provoke infighting... Unless it doesn't. I mean, Legate Lanius is surrounded by a myth of terror for a good reason. It would take a "very", very brave and charismatic legate to rally his own legions under his banner, charge Lanius for his failure at Hoover Dam and declare war to him. I mean, it's possible, but it's not a given.
About the NCR:
-How would they pay for such an invasion? Wars are costly, and the brotherhood made sure to cripple the West's economy when they bombed Redding. Fixing their economy was one of the reason why the NCR turned into an expansionist state. Thing is, at best, they "could" fix their economy thanks to Vegas and Hoover Dam after a few years, but taking over America? They simply don't have enough cash to pay the amount of soldiers it would take for such a massive operation.
About the Brotherhood:
-The actual brotherhood of steel, the one in Maxson State California, is in ashes. They are being exterminated by the NCR. Yet they are the only ones who "could" make a difference if they sided with the NCR, the Mojave Chapter is too small, too isolated, and mostly, it doesn't have much to put on the table. The NCR doesn't need them, unless for spec ops and for fixing power armors. When it comes to technology, the NCR has the Shis, who are superior to the freaking Institute in every single way when it comes to industrialized high technology. They actually produce power armors, railguns, they can maintain a functional AI, understand schematics for vertibirds and produce seaweeds that eat radiation. They mean business. Allying with the Mojave Brotherhood wouldn't give the NCR an army, it would "just" give them valuable spec ops.
-In terms of philosophy, the brotherhood and the NCR are total opposites. In the event of an invasion, the NCR will find nuclear weapons on its path. There's no way in hell the brotherhood would let such devices fall into the hands of a faction who wants to emulate the old world ; the brotherhood HATES the old world and wants to prevent it from rising up again. Infighting within this alliance is simply inevitable in the long term.
Like R Graves, I'd suggest you to come up with a brand new faction instead of using these old two ones. It would be way more interesting, more believable and easier to write too. If you want to include vault technologies, maybe a expansionist vault population, having access to a secret military tech unseen since then (bioweapon, mech, whatever) ? That would be something new. A vault conquering the world. Or a religious federation of tribes, made possible by some event with the daughters of Hecate and in reaction to the defeat of the legion. We haven't seen a proper religious faction since Fallout 1.