I’d suggest looking at the Interagency Appraisal Guidelines, specifically section XV on Reviewing Appraisals and Evaluations, which discusses Resolution of Deficiencies (XV.C) and Documentation of Review (XV.D).
If your bank’s review of the appraisal determines there are deficiencies in the appraisal, then you would follow the rules in Section C of the Guidelines. If a second appraisal is warranted follow your bank’s same independent process for ordering a second appraisal and reviewing that appraisal. The borrower needs to be separated from determining the value of the property.