Warning: SPOILERS AHEAD
I just did Bioshock Infinite followed by Burial At Sea: Wow what a saga. After having spent time trying to understand Infinite, which became clear after a while, I just think I cracked Burial At Sea.
It's both interesting and disappointing, but here is goes: Remember Dr. Suchong's Voxaphone quoting Einstein saying "The only reason for time is for everything not to happen at the same time"?
Burial At Sea is happening both before AND as a parallel timeline of Bioshock Infinites' Ending: it is one of the many "variables" of the scenario, which split happens when Comstock cuts the head of Anna then decides to go Rapture, and one of those timeline where one Elizabeth tried to stop Comstock from taking the baby (final flashback in BaS) and then tries (or another Elizabeth tries) to kill him.
This is a version of Rapture where, instead of Fink being inspired by the original Raptures' Plasmids and Eve, Suchong is the one being inspired by Colombias' Vigors & Salt.
This means two things:
1. Even though Elizabeth found a solution to stop all the Comstocks/Bookers timelines from happening in HER reality, all the other timeline where it has, is, and will happen still co-exist with this current reality.
2. That's why Bioshock Burial At Sea starts, when you exit the Office, with the same banner as found in the original Bioshock Lighthouse: "No Gods or Kings, Just Humans"
What Bioshock Infinite is about, is the fact that no matter the future Comstock sees as a self-declared prophet or even the multi-dimensional powers Elizabeth and the Luteces have, or even what the Plasmids/Vigors brought to the elite inhabiting new edens like Rapture or Colombia, they're still ultimately just humans living through one and only life and reality.
Now this Burial At Sea timeline can be easily explained: in her many attempt to stop future events to unravel in Colombia, Elizabeth tried to stop Comstock but at the moment he was trying to capture the baby, hence why the baby got it's head cut and Comstock went to Rapture. But then an Elizabeth from a very dark timeline (probably not the same one as in the flashback) went to rapture to have her revenge, and the only thing to discover is just that: how did this she become so dark?
In fact that maybe why we're playing her in Episode 2 and what's very interesting in this Bioshock saga: Elizabeth is not the usual "un-criticable princess to be saved" but instead is as much guilty as Brooker/Comstock for having used her power to manipulate time and try to prevent destined timelines to happen. In fact in both Bioshock 2 (with the grown Eleonor) and Bioshock Infinite (with old Elizabeth) they too end-up being very bad powerful being who would destroy the world. But as said above, she's just another human.