AA does not offer direct service from HNL to YVR. Did you perhaps have a connection via LAX? And did you actually receive a
ticket number (starting with "125") from BA?
In any event, since this involves travel from, to, or within the U.S., the U.S. Department of Transportation has jurisdiction. You can file a consumer complaint against AA, BA, or both with the DOT. More information about filing DOT complaints here:
https://www.transportation.gov/airco...umer-complaint
("File a Consumer Complaint")
And welcome to FlyerTalk!