Look I'm trying to be amicble here, everything you've said is pure speculation and it hasn't thus far stopped you; I am trying to judge your theory, a theory which is severly under-fleshed out. I cannot be persueded by half an arguement and what the Enclave wants to do is pretty fundamental to further speculation on it's composition. Your saying the group existing, your saying that they want to rule America - those are both speculation, all I'm asking is why which is pretty important.
Speculation is what we do and I seem to remember you doing a lot of it with us. We have blanks in the story, we have scraps of infomation therefore we build a picture from that based on what we have. I have my relatively simple theory, the War happened, the Government basically failed to maintain order, regrouped and slowly became the Enclave we see in-game; I have my evidence in-game and I am quite happy with it as an origin.
In my speculation, I also try to go by in game info, behavior, etc.
What you are asking for, is the origins of this group, what their agenda was, etc, and that is a whole new level of speculation, where I can't draw upon anything in game, because we don't know any details on the make-up of the pre-war government.
I will say this: the purpose of government, in the USA, is to serve the people. Officials are voted in by the people, local, state, federal. The Enclave does not seem to care about the people.
LT says well that is because they are not citizens. I disagree. There is nothing in the Constitution that says in a time of war, people cease becoming citizens. He also claims the USA ceased becoming the USA. Well, what makes us the USA? According to LT, it is the government. Again, I disagree, and say it is the PEOPLE who make the USA, and it is the government, created by and for the people, to serve the people.
The Enclave thus abandoned the people. By choice. They made no relief effort. They were in a position for peaceful relations with the people, but instead chose to serve themselves. Instead of say, researching a cure for "mutant problem" they chose to eliminate everyone, but themselves.
Anyway, I gave you a rough guess as to why this shadow government appeared. Possibly a power struggle with commonwealths and the fed. I'm going to assume they were on side with the commonwealths, only because, generally, corporations are in favor of a limited federal government and less regulation, and the Enclave clearly has a lot of corporate influence. However, it could be the other way around. I will assume that is correct though, as it explains the Enclave symbol of the stars surrounding the E.
Btw, that symbol is kind of a clue that the Enclave existed pre-war. IMO.