How it ends

Spoilers, if you haven't worked out for yourself that the British are going to get humiliated.

presumably by if not before the winter of 1862-63, Williams surrenders Lower Canada, Palmerston loses a vote of confidence (just like North and Aberdeen) and Gladstone comes to power and makes a deal rather than send good money after bad, as he did in 1881 in South Africa. At that point, it is an open question how long Gladstone can last, and the Conservatives and a realistic foreign policy comes into play under Disraeli.

In the meantime, once there's a settlement between the US and UK, a re-run of the historical 1862-65 campaigns of the US against the rebels get underway, except delayed by roughly 12-18 months, at which point the rebels surrender unconditionally in 1866-67.

Enmity between the US and UK lasts, however, and so there's no US assistance when a European Continental hegemon arises and then defeats the British in an analogue of the Great War; fascism arises in the UK in response and a British fascist government launches a revenge war analogous to the Second World War, the Allies blockade Britain and London suffers the first atomic bombing in order to end the second war. Millions die, but the world lurches into a more peaceful phase under the aegis of the US and various other great powers, none of which are Britain, since the island is largely an irradiated, diseased wasteland, inhabited by the starving, shell-shocked survivors of the Fall of the British Empire. Perhaps the surviving Irish will take pity upon them, but given the memories of the Famine, perhaps not.

And all because Palmerston tries to make political hay from a two hour delay in the mails. Sad. 

I'll say one thing for it: it's remarkably well spelt given that it was written with one hand. We should have all seen this coming, though, as the timeline's title gives us a clue that God (or the author, who may struggle with the difference) doesn't like those who meddle with the US:

I have read a fiery Gospel
writ in burnished rows of steel,
"As ye deal with My contemners
so with you My grace shall deal,"
Let the Hero born of woman
crush the serpent with His heel,
Since God is marching on