Sounds like what you are tyring to do is called Split Horizon DNS.

Requests from outside your network should revolver server.domain.com to the public IP, but requests from inside your network should resolve it to the private IP.

If that’s what it is then you register the public IP with your nameservers. You also run a DNS service internally which you point all your computers at (likely by putting it as the DNS server in your networks DHCP settings). That DNS server is set up to return the private ip addresses for all your servers, and to forward any other requests to some external DNS like 1.1.1.1