Question : Internal/External DNS Setup

Hello,

I have a few DNS questions for you experts...Just to give you an idea of my current topology:

Two internal AD/DNS servers in the domain corp.example.local.
External DNS entries are listed with GoDaddy for example.com.

I have 2 webservers in my environment, lets call them webserver1 and webserver2 both hosting a customized 3rd party application.  I have another webserver hosting my website, webserver3.  The internal DNS entries look like this:

DNS
|- Forward Lookup Zones
     |- _msdcs.corp.example.local
     |- corp.example.local
     |- example.com
|- Reverse Lookup Zone
     |- 1.16.172.in-addr.arpa

Here is my issue - I want to reconfigure the crummy 3rd party software to finally use the DNS name of my machine instead of being installed to the IP address; however I want the machine name to resolve internally and externally.  If I check my reverse lookup zone, I will see PTR record IP address 172.16.1.5 and the FQDN webserver1.corp.example.local.  If I check the forward lookup zone I see that the A record for webserver1 with the IP 172.16.1.5.  Currently, nothing exists for this machine in the example.com forward lookup zone.

Webserver1 is configured to a public IP address via an ARP entry in the hardware firewall.  My simple yet longwinded question is this: How would I configure the external DNS entry through GoDaddy to point to the same exact machine that the internal entry does and still resolve the name webserver1?  

It seems as simple as creating an A record on GoDaddy to point to the external IP of the server and give it the same name that I did internally, although I really feel like I am overthinking this and confusing myself.

Answer : Internal/External DNS Setup

I was thinking either adding the A record on Godaddy or creating a CNAME record, should resolve internal and external by the webserver name. If you have an internet facing address and it sounds like you do, should just be as simple as your thinking it is.