The easiest way I think to do this would be to set up three separate menu pages, so you have a different menu card for each location. Sounds like this is what you’ve done already.
You’re going to have to make extra categories. So ‘Classic & Custom Burgers’ as a category would become ‘Classic & Custom Burgers V/W’ and ‘Classic & Custom Burgers CP’ for the locations. So now you have two category options to check/include when you go back and edit the product.
Go back into your products and check the select products you want to appear in the ‘Classic & Custom Burgers CP’ by checking the relevant category in the edit product page then save.
So this category will be using the same products, but will have less of them in the list. Then on the CP menu page, add the category ‘Classic & Custom Burgers CP’ instead of the original category to get the reduced list. Do the same on the ‘Classic & Custom Burgers WP’ menu page.
Hope I’ve explained that clear enough, I was even getting confused whilst typing it 🙂