Unfortunately, there does not seem to be a clear answer to either of your questions, but I will do my best to address each of them based on the information I was able to find.
1) How far back does this alternative reality actually begin?
As far as I can tell, we can say that it must have started at the very latest when Connor was 4 (as according to the wiki, this is the age at which his mother died) - had the alternative reality started any later, Connor's mother would be dead in the alternate reality of the DLC. As to when it started, it's very hard to say - there does not seem to be information that indicates an exact starting point. However, based on the fact that the revolutionary war still occurred as normal, I would venture to say that the alternative reality of the DLC likely did not 'split' from the true reality of the base game much earlier than the death of Connor's mother. This is because had the reality split much earlier (say, centuries), there would be changes in reality that would have propagated throughout time, resulting in a significantly different alternative reality (i.e. there might not be an America discovered, or even a revolutionary war. Thus the alternative reality must be similar enough to the reality of the base game to have all these similar details).
tl;dr - The reality must have split (and thus begun) no later than Connor was at age 4 (according to the wiki, Connor was born in 1756, so no later than 1760), and likely not that much earlier than Connor's birth (since any earlier would likely lead to a completely different history and would probably change the entire setting of the alternate reality).
2) At what point in the main story do the events of the DLC begin?
Well, if the DLC occurs in an alternate reality, and we know that it could not have started later than the death of Connor's mother, then we can say that at the latest the DLC events take over when Connor is 4. However, I am not sure that this question can be answered - since they are two different realities, and we don't have a definite moment in time when the two realities 'split' from one another, we can't say with certainty when the DLC events begin. Thus the best answer I could give would be that the DLC universe events take over when the realities split from one another, which is no later than 1760.
Edit (based on OP's comment):
In order to become King Washington, he would presumably need to win the revolutionary war, which as I recall would occur after sequence 12. However, to address your question more directly - does the DLC take place during or after the main game - I would say that it occurs separately from the main game (and thus not before or after). Different timelines implies that different events must have occurred, so saying 'before' or 'after' does not really make sense when comparing events in the game.
However, from a dates perspective, since Connor was presumably born at the same time in both timelines, and since he is an adult in both sequence 12 and the events of the DLC, we can say that the events of the DLC likely took place around the same time as sequence 12. However, once again, since the timelines are different and have different events, in order to know if the DLC occurred before or after sequence 12 specifically, we would need more information around the dates in the base game and the DLC.
If this whole multiple realities concept seems confusing, that's because it is! I would recommend checking out this interview of cosmologist Sean Carroll explaining the overlapping of realities - pay specific attention when he begins using the cars metaphor.