I don't think you should copy your big boss

You big boss like your boss and they are same type of person. You should ask your big boss help to work with your boss when big boss talked about complaints from your boss. This kind of boss wants to feel the power of being boss. So let them play. Don't point out error directly especial in front of others. Use email but be gentle and humble. Email her back with details then stop by immediately to explain in oral. Don't let her have time to think it over and hate you.