[qualiteam]

When you click the "Recalculate" button it submits the form to the \XLite\Controller\Admin\Order controller class and runs the doActionRecalculate() method there.

The controller recalculates the values and returns them back to JavaScript (see the displayRecalculateData() and displayRecalculateShippingData() methods).

JavaScript is configured to react on these events and update the page. See these files:
- skins/admin/order/page/info.js
- skins/admin/form_field/inline/select/shipping_method/controller.js

I never tried to add custom fields on that page, but I guess you should a) update the doActionRecalculate() method in the controller and make it return your custom data; b) add a custom JS file that will update the page in a way similar to how existing info.js and controller.js files react on events from the controller.