Occasionally someone asks us why their online catalog calculated the "wrong" sales tax for an order when the customer is from a different province than the merchant is from.
We (Emerge2) are not tax experts, nor do we provide tax advice, but
our layman's understanding is that if a merchant sells goods to a
customer in another province and ships the goods to them in the other
province, then it is the other province's federal sales tax that you
need to collect and remit along with your "GST/HST collected"
remittance. So if the other province is HST-participating then you
collect the other province's HST rate for the sale, or if the other
province is NOT HST-participating then you collect only GST for the
sale. That's just the way we understand it. It might or might not suit
your circumstances. You might want to do your own research on the Canada Revenue Agency (CRA) website, get your own
tax advise on it, and make your own decision.
Here's some information regarding sales tax and other provinces on the Canadian government's website (CRA): https://www.canada.ca/en/revenue-agency/services/tax/businesses/topics/gst-hst-businesses/charge-collect-place-supply.html under heading "Place-of-supply rules".
The above link talks about the definition of "place of supply" (which province's sales tax applies when shipping to a different province or territory).
Hope this helps or points you in the right direction. There are many related links on these pages.
Please remember the above disclaimer -- this is not tax advice nor professional advice, since we are not tax experts.