Craft Commerce multisite, different tax rates
As of Commerce 2.0, there is no support for multi-site apart from a product’s custom field information.

A cart exists in the session, once per Craft installation, and there are not separate carts per site. 

Multi-site is something we plan to add in the future.

Having said that, a cart stores the current orderLanguage based on the current language of the site the order is being made in. A custom adjuster could be written to add custom tax costs based on this information: https://github.com/craftcms/commerce/blob/develop/docs/adjusters.md