You are correct that only Congress has the Constitutional authority to remove a sitting President. Congress can do that by Impeachment. But Congress cannot remove a usurper by impeachment.
The power or authority to remove an usurper from the White House, via Quo Warranto, was delegated by Congress to the District Court, Washington, D.C.
To sue the President of the United States via Quo Warranto one must have standing. But the thing about Quo Warranto is that the President must PROVE he/she is eligible to be President.
The best way to resolve the birth certificate issue is via a subpoena for his original birth records to be examined before a Grand Jury.
The COLB is the default birth record you get when you order one. By law, the HI DOH has to provide any copy of any certificate if you specifically request your original, long-form certificate.