Ok, so I found the International Olympic Committee official document about the Tripartite Commission. Their sole job is to give Olympic positions to nations with low or no Olympic participation. To be eligible for a position, the nation must have averaged 6 or less athletes in the last 2 Olympic games.
This is not Ireland, so Dolly definitely will not be one of these positions.
Most likely the 3 wrestling positions will go to an African or Asian nation with an underdeveloped Olympic program who had individuals that tried unsuccessfully to qualify the normal route. So MattM was definitely on the right track.