Include the pushSite URL query parameter to specify site context when performing an external REST call. Include the site as the value of the pushSite parameter. For detailed information about the pushSite parameter, refer to Multisite Request Processing section of the Platform Programming Guide.

For example, to set the site context to mainStoreUS:

curl -L -v -b customer_cookies.txt -H "Content-Type: application/json"
"http://localhost:8280/rest/model/atg/rest/ShoppingCartActor/
totalCommerceItemCount?pushSite=mainStoreUS"