Ignore domain cookie for some services in the same domain?

The HTTP spec does not allow you to know which cookie is for which domain when it is arriving into the server. The browser will present a cookie with the same name twice. Once for domain.com AND site2.domain.com

Your alternative is to use an HTTP_RESPONSE event and check if a Set-Cookie header is present when the cookie is being created and then CHANGE the cookie to a different name. Then you would have code an HTTP_REQUEST event to reverse this logic so as to pass the original name to the backend server.