to anticipate = to predict, to guess what was to happen
a facet of = an element of
the assassination = the plan to murder the political leader
which was to give the next three days added poignancy= which made the next three days extra important, gave the next three days a new relevance.
In summary, Ethel's substitute was the first person to realize there would be a specific element to the plan to kill (insert person to be assassinated) which would make the next three days particularly important.
(presumably something would happen within the next three days enabling the success/failure of the assassination attempt which no one had noticed before)