New Login Page

Our SharePoint 2010 environment have 1 web application which is configured as:

1) Classic Mode Authentication

2) Enable anonymous access. Unchecked

3) Integrated Windows authentication

4) Negotiate (Kerberos)

everything works great on the network, users transparently authenticate to the site and never get a login pop-up

Now, that users want to use SharePoint from home from personal/company owned machines. they access the site and a pop-up message shows up so they can put their user name/password which for some reason it seems complicated for them. so the question I have is can I create a new Claim based web application as FBA with the same web address/or new one that have a normal login page (1 page only, no SharePoint features) so they can put their user name and password and once they authenticate the page logs them to our Intranet SharePoint?

thanks

Noor