Website Virtual Directory / Website Setup

[captnops]

I have application websites that we were hitting using the IP address of the public interface, and 1 that we use SSL, for example:

http://1.2.3.4:2004/ph82/TRM

http://1.2.3.4:2004/ph82/TRM2

https://1.2.3.4/ph82/TRM3

We have just registered a FQDN for this site and would like to be able to access it publicly by using:

http://mydomainname/trm

http://mydomainname/trm2

https://mydomainname/trm

(somehow aliasing the port 2004 and the /ph82 for the non-secure sites and aliasing just the /ph82 for the secure site)

Could someone point me in the right direction?

Thank you