IIS Integrated Windows Authentication Question

Question

Hello,

We're running an IIS server that's hosting a site and we're trying to get Windows Integrated Authentication to work on a site for internal use. The issue we seem to be having is that we've configured the DNS name in ourdomain.ORG, while our computers are in an AD domain called ourdomain.LOCAL - so when we go to https://site.ourdomain.ORG, we're getting prompted for credentials. If we go to https://hostname.ourdomain.local, we're automatically logged in.

Is there are a way to get Windows Integrated Authentication to work in this scenario?

Thanks