Re-directing (or mapping) a subdirectory inside multi-site

Domain Name:
Domain & hosted both on HostGator
(and is primary site on multisite install for subdirectories)

Domain Name:
Hosted on GoDaddy

File located on on HostGator:

I want to be able to put in:

and have it take me to the

I have confused myself on the best route to take. and I'm totally new to multi-site so my head is about to explode.

Domain mapping? Multi-site?