I have a website "example.com" that is hosted in a subfolder of another domain "example2.com" (GoDaddy shared hosting).
So if a user were to go to "example2.com/subfolder/website", it would look the same as just going to example.com.
I believe you've misunderstood how multiple domains work on shared hosting (or any other type of hosting).
1) your root directory (main user) is actually one directory higher in the path than your primary domain.
2) for a second (or more) domains to be hosted a sub-domain is actually created, rather than a sub-directory.
3) if sub-domain is failing (allowing the path access via the other domain), than you either have an issue with your host or an issue with DNS propagation.
4) It's my opinion that your simply confused over what your seeing in the GoDaddy Control Panel.
My suggestion to you, is use another computer and another IP to determine if your actually able to access VIA HTTP, and NOT the GoDaddy Control Panel.
example2.com/subfolder/website/example.com
FWIW I did some work last year for an org that had a sub-domain via multiple hosting and using GoDaddy last year.
The primary account holder had a dozen domains, and the domain I was working on was an additional sub-domain. Logging in required using the primary users name and password, which is bad judgement on the part of both the primary and secondary users. Somehow, GoDaddy was able to distinguish these different domains in billing.