I note that you raised two quite separate strands of thought amone those not wanting to be governed from Ottawa:
Independence. I.e. Alberta becomes a sovereign nation. How that would work only its residents can decide.
Change of nationality. I.e Alberta becomes an American state, not independent at all, and subject now to a different policies, laws, public services, etc. Alberta has a border with the USA's Washington state, but is otherwise surrounded by Canada, along borders defined simply by longitude and latitude lines.
One effect is that Canadians travelling between British Columbia the rest of the Southern half of their country, would be crossing into a foreign country and out the other side.
I think the USA option raises another practical point. I believe Canada fully uses the SI units of measure, as the UK does for almost everything. The USA insists keeping the Imperial units (it calls them "American"), outside of science and engineering. I wonder how that would work? ..
Secession calls are quite common around the world. The Basques in Northern Spain, Scots and Welsh wanting to dis-unite the United Kingdom, various European and Asian lands with their own motives.
Nationalist sentiment in Northern Ireland is different though, wanting to merge with Eire; more like the Albertans wanting to become American, though with more historical logic.
The difference is that those Irish and Canadians want to join established nations.
Full independence is a very different matter. "Newania" would need establish and pay all by itself for its own:
Its own currency and fiscal system,
Security services, Customs, Police and Judiciary,
Civil Service,
Legal system including national laws on e.g. enviromental protection that could affect the neighbours,
Education, health and welfare services - buildings and personnel, and benefits systems.
Postal and telephony services,
Motor-vehicle and Driver Licencing and taxing,
Military services,
Roads, railways, airports, harbours (Alberta is land-locked; Wales, Ulster and Scotland are not).
Electrical and gas networks,
Diplomatic services and missions.
It would have to negotiate new relationships with its neighbours including the nation of which it was once part; and its own memberships of a slew of international bodies, treaties and alliances. (The UK belongs to about ninety of these, e.g. UN, NATO, ISO, MarPol, ...)
All difficult and expensive; and made more difficult by risking peculiar mis-matches in laws, etc; a result of over-"devolution" in the UK.
Fine if Newania has a sizeable population and thriving industry that can export lots of goods and/or services. If not, it could really struggle if no longer supported by the rest of its erstwhile nation and having insufficient resources and income for self-support. For our own example, Scotland might make it alone but I doubt Wales could.
(European secessionists wanting their Newlandia to join the EU, are gambling first on being allowed, and secondly, being supported by taxpayer-funded grants from the rest of the bloc. I do not know if an American Alberta would receive parallel support from the USA at large.)
I fear many of the breakaway calls in some countries are from a mixture of "greener grass" disaffection, historical grudges that really should be laid to rest, overweening optimism, and pure romanticism based on centuries past.
