Shawn Grate v. Ohio

If a criminal defendant, charged with a death penalty-qualified offense, admit to murdering multiple women, and the only possible defense is a verdict of not guilty by reason of insanity (NGRI) and/or a mitigation case based on a mental health diagnosis, will the defendant be deprived of a the Constitutional right to effective assistance of counsel and procedural/substantive due process if trial counsel withdraws the NGRI plea before trial and fails to present a full mitigation case -- even if the evidence of defendant's guilt is overwhelming?

If a trial court bars mitigation testimony from a defendant's family member, and rules that testimony about the defendant's mother is inadmissible and that much of an expert's testimony should be disregarded by the sentencing jury as hearsay, does it constitute a due process violation in a death penalty case?