How to setup connection broker HA DNS name for internet access

I am trying to setup an RDS farm high available that can be access from internet, My gateway dns is RDS.mycompany.com and my connection broker load balanced dns is  RDCB.mycompany.local. This setup works fine when accessing the RDweb from the lan but fails from the internet. I think that is because the  RDCB.mycompany.local registry does not resolve any thing from the internet.

And this bring me a question if the users from the internet must have the dns records pointing directly to my RDCB and what ports must be open from the internet to the RDCB or how do I need to setup connection broker load balacer DNS