Civicrm altering contribution page
How many different tax rates are involved?

It there aren't too many, a no-tech solution would be to create a different price set for each different tax rate and have province-based links on your call to action page.

Added later:

I don't know a lot about the tax feature but I put down what I think might work. (This is all untested so could be totally wrong.) Assuming you have already ticked enable  tax and invoicing at Administer > CiviContribute > CiviContribute Component setttings, I would have thought you might need to:


create three different financial account with the different tax rates say tax2, tax3, tax4.
create three different financial types member_dues2, member_dues3, member_dues4
edit the three different financial types  to link each to the appropriate sales tax account
edit the three different financial accounts you will now have, to set the account code to the same value for each so that that membership revenue can totalled across aall the provinces using a line item report  (if this is a what you need.)
-Create a price set for each province lined to the correct financial type.


If this doesn't work, my apologies, but it may help you on your way somehow.