But they won't be one single country is the point I am making. You seem to assume that union is inevitable.
It's not inevitable. It's just one of many possibilities. (with the range of possibilities increasing the further back one goes). If the South won its rebellion against the British, Columbia would not have been united, presumably.
But Canada formed in response to the US existing so how can something similar happen without the same political pressures of an existing US?
I'm not sure you're quite understanding what I'm trying to say.
You need to explain, STEP BY STEP, how several separate colonies develop in such a way that political union becomes desirable and is successfully implemented without there being any obvious external or internal pressures to do so.
1. In the aftermath of the (in TTL, failed) ARW, to solve the issues that led to it, self-government, and increasing economical power gave them more
de facto autonomy than they had on paper. (the factors behind this reality got stronger and more important over time). It was their privilege as, arguably, the most important part of the British Empire outside of Britain itself.
2. The South, historically the most pro-British region, got estranged after the British forcibly abolished slavery in all of Columbia. They even rebelled against the British, but with the Northeast's support, it was crushed. In the aftermath, they moved it closer to the Midwest, economically and politically.
3. The Midwest and South soon eyed Mexico's land, and they invaded in 1840. They won but it took longer than winning the OTL Mexican-American War did for the US. There was dispute over the spoils, and in the aftermath, war threatened between them. Thus the British solved the issue by making the gains be part of a whole new dominion. This annoyed both the Midwest and the South, which gained little in the end, but the British did get a dominion that was, relatively, very supportive of them. Columbia West soon got rich off the California gold rush, which intensified the unhappiness of the Midwest and South.
4. The events surrounding Columbia West led to Columbia Midwest and Columbia South to strengthen their alliance further, and with the pan-Columbian movement getting stronger as well, the biggest obstacle was the Northeast holding out. Hamilton's successors grew more and more amenable though, and the thought of the combined country's economic power only increasing the influence of ports like New York, Baltimore, and Boston steadily convinced the Hamiltonian big business elite to get fully on board with the pan-Columbian vision.
5. Eventually the West was convinced to get behind Lincoln's vision thanks to the promise of a transcontinental railroad. Nonetheless it was the most reluctant of the four. In 1865, the four Columbias agreed to send Britain an ultimatum - a union of the Columbias into one united nation, their own head of state (which nonetheless could come from the British royal family), and a 50-year alliance with the British, to sweeten the deal with London. The British had no choice but to accept. The Kingdom of Columbia formally came into existence in 1867, after a constitution was agreed upon.
6. Columbia, thanks to the aforementioned autonomy, is almost as much of the immigration magnet that the US was in OTL. Its industry and agriculture grew rapidly for much of the same reasons as OTL America did - the natives, unfortunately, do not fare much better.