name on the security certificate is invalid

I set up an SSL Certificate for my website. All works fine when the
site is accessed via

The problem is that there are many internal users and I don't want
them to have to go out to the internet to access the site. They
access the site with http://servername. This causes the error "name
on the security certificate is invalid".

What's the best solution for supporting both internal and external

More info:
1. For the internal users, the connection doesn't necessarily need to
be encrypted
2. On the website, I have "require ssl" checked (in IIS). Then, I
use a custom error page to redirect people to https if the come in to
the sive with http. I'd like to keep this part. It works well.
3. Is there a way to allow internal users to type and
have the router (cheap home router) keep the traffic inside the
building without going to the ISP and back?
4. Is there a way to install a second cert with the server name?
5. I guess I could maintain two copies of the site - one for internal
and one for external customer... but I don't like this solution. Does
anyone else do this?
6. Is there a way to make a single cert work for and
"http://myservername";? What about when people hit the site using just
an IP address (internal or external)?

That's it for now - any help would be greatly appreciated.