Login dialogs via VPN only for ONE single Web Application, But not any others?

We are using SharePoint 2013 Enterprise with service Pack 1 as our Intranet collaboration platform e.g. (http://Intranet.Domain.com/).

Details: - Our SharePoint Intranet web application uses: Integrated Windows Authentication NTLM.

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  Our end-users come to the company > They login to their computers (Windows 7 or whatever ) using their valid AD accounts e.g. (Domain\UserAccount) or UserAccount@Domain.com > They use only Internet Explorer > When they open our Intranet site: (http://Intranet.Domain.com/) > Everything works OK without any login prompts on pages nor documents at all.

  
  


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  All our end-users use Internet Explorer, and our Intranet site is the hom page

  
  


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  We have a set of defined GPO rules and settings which includes:

  
  

Local Intranet > All the "Automatically Detect Intranet Network" options. Also, On the added Websites, We have: http://*.Domain.com/

• We do not use https at all.

Issue/Problem: - Many of our end-users are working remotely, and they are using VPN > They use only Internet Explorer > When they open our Intranet site: (http://Intranet.Domain.com/) > A single login prompt will appear and the user must enter his/her account's info again (How to eliminate this?)

• Once again, If user is connected via VPN and clicks on document file > A single login prompt will appear and the user must enter his/her account's info to be able to access the file. Most importantly, Everytime a user clicks on any document file > A login prompt will always appear (How to eliminate this?)

Attempts: As I stated above that our GPO applies all the necessary settings in IE, and I tried the Windows Credential Manager (From Control Panel) to store credentials, Nevertheless, The login prompt will still appear for te pages only once and for the documents on every single click.

Also (http://www.sharepointdiary.com/2012/04/sharepoint-keeps-asking-for-password.html) did not help obviously.

VERY Strange Surprises:

A) A host-named site collection witin the exact same our Intranet Web Application but obviously has a different URL i.e. (http://Other.Domain.com/) is accessible via our VPN normally without any login prompts on pages nor documents at all !!! How come?

I mean, This is a site collection hosted inside the exact same our Intranet Web Application works perfectly fine via VPN without requiring any logins whatsoever.

B) All the other Web Applications, MySites, Other Site Collections that are running on the exact same server are ALL ACESSIBLE with ALL their documents without any login prompts on pages nor documents at all !!!

C) We have an Intranet test environment that is as far as I know 100% identical to our Intranet production environment, the exact same structure, deployments and settings, yet all the Web Applications, Intranet site, MySites, Other Site Collections are ALL ACESSIBLE with ALL their documents without any login prompts on pages nor documents at all !!!

Questions:

1) Am I missing anything? Have I misconfigured or need to fix something in our production Intranet WebApplication?

I compared the IIS settings/properties, NTLM,...etc and they are the same in test and production.... Why it works ok with the test environment but not with the production?

2) What can be done to completely stop/remove/eliminate these irritating login dialogs for our end-users whom are working remotely via VPN ?

I would really appreciate your inputs and suggestions !

Thank you !