What stories handle interstellar distances without cheating on relativity or causality, and without localising the conflict to avoid causal separation?
These two criteria together are narratively inconvenient, to be sure. "Causally separated conflict" almost sounds like some sort of lit-crit hoax. So far I don't know of any example.
Note I am not asking that the author handle the issue well. I'm really just asking for stories which somehow manage to meet those two criteria (which are focused and fairly objective, and I elaborate on them below). The question of how one should follow the author's examples and/or learn from their mistakes is separate!
The standard way to deal with interstellar distances is some sort of warp drive or hyperspace or other cliché. There are sub-light interstellar examples, such as the handful that are listed under "Which sci-fi universe has the slowest extensively used interstellar drive (best available)?", but even those get mixed with FTL or have other forms of cheating. For instance, Ender's Game has nearly-as-fast-as-light travel and even time dilation, but it also has FTL communication. (And later, some strange psychic stuff happens.) Chronicles of Solace (from the description, I haven't read it) has sub-light travel combined with time travel.
All of that is cheating on relativity or causality: there's to be no FTL travel or communication, and no backwards-in-time travel or communication either. (And psychic stuff also counts as cheating, if it effectively involves FTL or backwards-in-time messages.)
One answer to the above-linked question observes, "Most other universes in which FTL travel doesn't exist generally confine travel to members of our own solar system...", Even in those that do involve more than one star system (without cheating), the plot is still localised. The conflict never gets causally separated in these cases.
[See wikipedia for both these terms -- I can't post more than 2 links. Basically, the action is separated by the speed of light. (At least) two significant plot events happen that are far enough apart in space, and close enough together in time, so that you couldn't get from either event to the other at light speed or slower. So, if there is no cheating, neither can properly be said to happen before the other, nor can they be properly said to happen at the same time.]
Generally, in these non-cheating interstellar stories, all the action is in one star system and the others appear just as part of the backstory or scenery. Another option is that the story is in two or more acts, each act in a star system, with many years lapsing in between, so there is no causal separation. A different example from Wikipedia's list of sub-light interstellar travel is Tau Zero. It seems (from the description, I haven't read it) there is no cheating here. There are extreme distances, and extreme time dilation is the central theme. But the story happens entirely on the one ship.
I did look at each examples on the two lists at least briefly, and as far as I see everything fails one criterion or the other.