The AP needs to file a claim for benefits in order to get benefits to which the AP is entitled. The information provided doe s not assure that there was a QDRO or that the AP was entitled to anything. It also does not allow an answer to the "Who is wrong?" question, although it appears, with only imagined doubt, that the participant is not involved.
You may need an ERISA attorney involved. But it sounds like the Plan Administrator (PA) incorrectly paid the APs portion of benefits assigned by the QDRO to the Participant. The PA would likely be on hook for making the AP whole and then trying to recover the over payment to the Participant on behalf of the Plan.