Active Directory Split-Zone vs SubDomain Domain Name

Solution 1:

There is absolutely no reason to use the same AD domain DNS name as your external web-facing DNS zone. None. At all.

Microsoft recommends using a subdomain of an existing domain, so something like corp.yourdomain.com or ad.mydomain.com is fine. If you don't want your users to see that their login name is corp\user you can set the domain's NetBIOS name to MYDOMAIN during the DCPROMO process of the first DC in your domain. The end result would be that your domain's FQDN would be corp.mydomain.com but your users would see mydomain\user. This way you can have "prettier" logins, without the complete shitmess of split-horizon DNS.

Seriously, there's no valid reason to ever have split-horizons DNS with your AD infrastructure.