If you shoose host the DNS zone of your domain in another DNS technologie like GoDaddy in your case , you have to allow domain controllers to register their own SRV and A DNS records.
I think your design is complicated to be impleted and not recommended for the following reasons:
Create and manage manually SRV and A records for domain controller is complicated, because there is SRV records depends on the domain controller site and when you move a domain controller to another site this kind of records must be updated automatically, below a idea about the list of SRV records generated automatically by a domain controllers:
LdapIpAddress A
Ldap SRV _ldap._tcp.
LdapAtSite SRV _ldap._tcp.._sites.
Pdc SRV _ldap._tcp.pdc._msdcs.
Gc SRV _ldap._tcp.gc._msdcs.
GcAtSite SRV _ldap._tcp.._sites.gc._msdcs.
DcByGuid SRV _ldap._tcp..domains._msdcs.
GcIpAddress A gc._msdcs.
DsaCname CNAME ._msdcs.
Kdc SRV _kerberos._tcp.dc._msdcs.
KdcAtSite SRV _kerberos._tcp.._sites.dc._msdcs.
Dc SRV _ldap._tcp.dc._msdcs.
DcAtSite SRV _ldap._tcp.._sites.dc._msdcs.
Rfc1510Kdc SRV _kerberos._tcp.
Rfc1510KdcAtSite SRV _kerberos._tcp.._sites.
GenericGc SRV _gc._tcp.
GenericGcAtSite SRV _gc._tcp.._sites.
Rfc1510UdpKdc SRV _kerberos._udp.
Rfc1510Kpwd SRV _kpasswd._tcp.
Rfc1510UdpKpwd SRV _kpasswd._udp.
I think also , exposing a domain controller to internet is not a secure design. It's recommended to Install the domain internally and let the clients contact domain through VPN ( a secure connexion).
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