Say they were visiting, (and had indeed been back within the last couple of months) and cash the cheque. I'm not condoning it, just saying I've seen people not switch insurers when they were supposed to, even for years. Obviously if you're in the system and have a principle residence in the other province then crash you'd be in trouble.

There are a whole bunch of issues. An insurer taking a premium and giving an insurance certificate does not guarantee coverage when a claim is made. If the insurer believes they were mislead or lied to when the policy was taken out, they may refuse to pay. If there is a third part injury and a lawsuit ensues, the at fault driver may end up on the hook, this would likely follow them anywhere in Canada. Not a good way to start out.
By and far the best bet in my view, easiest and safest, rent a car one way, or as has been suggested a motorhome and drive across. No question of having an improper registration or finding out you don't have valid insurance.

Can you live in one province but buy a car in another?
I have an address in BC, which I can use as my home address. Can I buy a car in NS but use the BC address to insure and register the car, or would I need BC plates?

Read post #6 again.
Yes you can live in one province and buy a car in another but its not that simple and not the norm for Canadians to do so.
Renting would be easier but at what cost and for how long?

You can, but not sure how you would register it, as you would have to do this through an ICBC broker in BC and get BC plates and insurance. ICBC are very fussy, you would be best to call them and ask, but I doubt it would work.

Why wouldn't the insurance pay out? I've claimed, I got paid.

Similarly, how is buying a car in NS, registering it to the hotel and immediately changing the registered address to BC a problem (other than being a bunch of administrivia)?

I don't think renting the camper works, I think it would be cripplingly expensive.

The pickup truck RV thing looks good for its size too. Quite surprised when I looked through the pics for it.

The OP could hire a Ford Transit, buy a Gaz burner and chuck a foam mattress in the back. Its just the oneway penalty that gets you when hiring vehicles in NA.

As mentioned above, here in Saskatchewan, when you renew your insurance, you have to declare that you're living in the province and not spending long periods outside it (I forget the exact wording). If they lie, they're presumably committing insurance fraud.

You will need an address in NS to register & insure the car. Be sure to read the insurance contract small print.

Once you arrive in BC & settle there, you'll need to re-register car & swap your DL from NS to BC. And advise yr insurance company of your move.

There are also several options where one can sign up to drive Other People's cars x-country; again, I'd advise looking at insurance small print.

They would need to cancel the insurance they have and take out a policy with ICBC in British Columbia. It is quite possible, due to the short time frame they owned the vehicle they would be charged the 12% provincial tax on the vehicle as well when registering it.

ICBC is the mandatory insurer in BC for all basic and liability. Not all third party insurers offer add on policies for BC.

What they propose in my view is quite unworkable and at best way more expensive and harder than renting. Or just fly to BC, settle in and then take a long vacation. There is bugger all to see for a good half of the drive from east to west anyway.