“In my humble opinion, impeachment and trial is the only JUDICIAL...”
Is Impeachment conducted by the Judiciary? No, it is conducted by the Legislature. It can not be considered “Judicial” because it is not.
Ineligibility is a matter of law. Matters of law are for the Judiciary.
Article II § 1, cl 5 specifies “no person [] shall be eligible to the office of President”, not “no person [] shall be eligible to election”. Election does not launder ineligibility.
You don’t believe that the Chief Justice is a part of the Judiciary? Is the Chief Justice part of the legislative branch? Does the Constitution mandate that an impeached president be subject to TRIAL in the Senate to determine guilt or innocence?
I might agree with you and I could see some judge somewhere conceivably going along with the position that Obama is not the President if he had never been sworn in, if Congress hadn’t sent him hundreds of bills to sign into law, if the Supreme Court had refused to rule on the constitutionality of his policy initiatives, if the Senate had not confirmed his cabinet and judicial nominees and finally if opposing candidates and opposing parties had filed suit challenging his eligibility.