yes on the DNS answer.
On the public Internet, you need to resolve your moodle to your public IP address; on the private intranet, you need to resolve your moodle to your private IP address.
For example, assuming your public IP address is 204.116.116.116 and your private IP address is 192.168.0.10: your public DNS server should have an A record in the mine.net zone for mymoodle to IP address 204.116.116.116; your private DNS server should also be setup with a zone for mine.net and you should create an A record for mymoodle pointing to 192.168.0.10.
Oh yeah, if you need to setup a private DNS server to accomplish this, you must point your PCs to this server for their DNS resolution. This also means you must configure your DNS server with Forwarders to look at public DNS servers.
General help
Can't access Moodle from inside school network
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