I am typing the web address and not the IP address
Do a nslookup from inside of the network. Is the result the public or private IP address of the server?
Well the difference is that the SSL certificate from outside the network is the correct SSL certificate and the internal one is the old non-SLL certificate and that is the issue I believe so the question is where do I go to update that?Remember that you said that the IP addresses you're getting as results are different based on whether you're inside or outside of the network.
Do you use exactly the same URL to access the site from inside and outside?I know you've answered yes to this. Is there an entry for this site in your internal DNS? If so, what happens if you take it out?
Also, when you try to access the site from inside the network, are you going directly to the internal IP address?