Users from other forest prompted for username and password

Hello Community

    Using Sharpoint 2010 Server and the UI the intranet has a one-way trust relationship setup with another forest so that users in the other forest can  access the intranet.

    As the creator I can log directily onto the Sharepoint 2010 Server and type in the url of the intranet and all of the web application pages that make up the intranet are returned to immediately when I click on any link on any page and I am never
prompted for username and password (no one should ever be prompted for username and password).

    But when a user logs onto to the intranet from another computer as a trusted user from the other domain in the one-way trust from the other forest, a prompt appears asking for username and password.

    Once the user provides the username and password the page is returned and they're logged onto the intranet. Now that page has links to the other web applications tht make up the intranet but when clicked on the link containing the url to those other web applications that make up the intranet the prompt appears again for the username and password to be entered and when the username and password is entered the other  web applications web page is returned.

    After that no more username and password prompts appear, unless the close button is clicked on the intranet page, after that retrieving the browser and entering the url for the intranet into the address box again  is when the prompt for username and password will appear again.

    Note: On the DC, Sharepoint 2010 Server and the user computer in "Internet Options" in "Security" the url to the intranet appears in "Trusted Sites" and the Security levels bar is set to "Low".

    So the problem is why when the user from the other domain in the other forest in the one-way trust relationship enter the url for the intranet into the address box of their computer is being prompted for username and password when they logon but when I as the creator of the intranet log directly onto the Sharepoint 2010 Server the
intranet page is returned immediately?

    P.S. I wonder is there anything in Web Config or IIS  or <identityimpersonate="true"/> (the web application were created using the UI not programmed)that overrides authentication?

    Thank you
    Shabeaut