For a special "affialate" solution, I am planning to run a webshop under multiple domains. I found out yesterday that when the cart is updated, ie a product is added to the cart, a product is removed from the cart, and when the user clicks on Checkout, the default URL of the website is loaded. This is something I don't want for several reasons: I am using ThemeKey to apply a theme based on the server name, and planning to add an affiliate ID to the order based on it, too, and also when the URL is changed during checkout, an error is displayed.

How should I modify commerce cart, or what is the correct way to do this?

Thank you very much for your answers in advance.