If you need your internal users to be able to browse external websites using your domain name, then the easiest thing to do in your circumstances would be to add static host records to your internal DNS server. You don't want to re-point your internal users to an external DNS server, because then they would not be able to resolve internal host names. So, for example, if you have a website
www.yourdomain.com, and you want your internal users to be able to resolve that name to browse that site, you would add a host (A) record to your internal DNS zone for the host name "www" and point it to the external IP address for that website.
