How do I update core in commerce 2.x distribution?
Simple solution found in the end. Before running a composer command I had to add paths in my Windows Environment path variable to both the Git.exe file and the ssh-agent file. 

I then ran a slightly different composer command from the one above:
composer update drupal/core --with-dependencies
I did this from the root of my site.

I had to make sure that drupal/core is in the require part of the composer.json file and not the replace part.