The due process Trump seeks ‐ notice, hearing, fairness, counsel, cross-examination, confrontation, neutral judges ‐ is only relevant during a trial. The House does not conduct trials; the Senate does. There and only there ‐ if we get there ‐ will the president have his due process rights.
But, as Napolitano himself notes, the House has rules, and one of those rules says that in the absence of a clear legal guideline, House precedent should be honored. The House may not have trials, but it is capable of witch hunts and inquisitions. President Trump is entitled under House precedent to the same process, including due process, that Richard Nixon and Bill Clinton got. Until the impeachment inquiry against President Trump, the House honored the tradition of relying on precedent as a guarantor of fairness: