Control Modules within the store pages?

I see no method for controlling what pages a module displays on once a visitor is within the store.

Example: I have the shopping cart module display in the right column while a visitor is shopping.
But once they click "add to cart" the module is still there. this of course makes no sense. We don't need a shopping cart summary module on the right hand side of the shopping cart itself.. That's redundant and confusing to the customer.

Normally this would be managed by assigning a module to a specific menu item,, but since there are no menu items for each part of the store I don't see how to do this.

I tried to make a dropdown sub-menu which would include parts of the store, but I had two problems with that.
- there seems to be only one "store page" available,, which is "checkout"... I would like to be able to control module display for all aspect of the store(categories, product listing, individual product pages, cart, etc)
- Even once I made a submenu for the cart.. yes the module won't display if you click directly on that "cart" menu item,, but it still displays if you reach the cart via "add to cart" buttons.

See page here: wideawake.us.cloudlogin.co/index.php/hika-shop/checkout