Not sure I understand the question.
What do you mean by One DC is not correctly
recognized in the DNS as an DC?
a DC requires a Same as Parent A record, an A record for its true
name, a NS if its running DNS, a GUID under _msdsc, and a _gc record
if it is a GC. Are they all missing? What happens when you do a
/ipconfig /reigsterdns and then restart netlogon service?
What are we solving for here? Is there an event or something showing
the failure? Is there a firewall between the DC that is failing? FRS
will start on a new port each time the ntfrs.exe service starts. If
its behind a firewall, you may need to lock down RPC and open some
more ports.