After the war began, what did the British decide their goal(s) was? Did they want to make the US British colonies again? Did they want to make them a vassal state of sorts with regard to commerce? Did they just want to knock the Americans down a peg?
They wanted to defend Canada and their overseas trade from American aggression. Great Britain did not start the War of 1812, the United States did. Great Britain did not plan to invade the United States or any of its territories, but the plan from the United States was to invade Canada, and worry about what to do with it later (it was an unsettled political issue with many considering annexation and others considering the territory as a political bargaining chip, and it all means very little because the US didn't capture any meaningful amount of territory during the war).
Great Britain was too busy fighting Napoleon to worry overmuch about invading the United States.
This is my flairea, I have written extensively about the causes of the War of 1812:
American war aims in the War of 1812
On British support of indigenous goals
Was the War of 1812 motivated by US expansionism?
Why did the British give Maine back to the US after the war?
I'm happy to answer any followups you have.