An do you have a business connection, is it static? Do you have more than 1 IP address? I fail to understand how anyone that does not even understand the basics of DNS in setting up AD or for their local network, would want to host dns to the public for their website -- that has what 1 IP address, 1 host? Be it an outside host or even if hosted off your own IP.
As already stated your confusing the requirements for getting the public to the IP your website is hosted, or any other service for that matter ftp, ssh, mail, etc.. an DNS in reguards to Active Directory.
Rarely would you ever host public DNS on your DC.. As to hosting it on your own network to the public -- to be honest there would be little advantage to you doing such a thing, only issues an complications. How many hosts do you need to provide dns for?? 1 maybe 2, with what maybe a mx record? What advantage do you see to hosting this on your own machine?

In a AD setup, all machines that are members of your domain need to point to the DNS for your AD, normally in a small to medium setup this would be the DC, or multiple DCs in a bigger setup.
This is like the #1 issue people have with AD.
http://support.microsoft.com/kb/291382Question: What are the common mistakes that are made when administrators set up DNS on network that contains a single Windows 2000 or Windows Server 2003 domain controller?
Answer: The most common mistakes are:
• The domain controller is not pointing to itself for DNS resolution on all network interfaces.• The "." zone exists under forward lookup zones in DNS.
• Other computers on the local area network (LAN) do not point to the Windows 2000 or Windows Server 2003 DNS server for DNS.If godaddy's total control DNS does not provide you with the dns features you need/want -- then find another DNS host.. Dyndns comes to mine, or
http://www.zoneedit.com/ they provide free DNS for up to 5 domains, they even support SPF records, etc..
I maintain dns for a fortune 500 company, both the internal an external.. I am quite familiar with the working of DNS be it BIND or MS, etc. An I would never in a million years think to hosting my own dns on some soho connection. There just is no point to it!!