You can use Cloud 9 Limo or Charley's Taxis. Cloud 9 is recommended by Aulani and offers a discount. I paid $120 each way(for a dedicated car) and they picked me up at the gate, took me to baggage claim, and waited for me to get my bags. Other people have taken Charley's Taxis, but they get mixed reviews. I believe they charge $55 each way to Aulani.
I found it cheaper to rent a car at Aulani for the days I needed it versus renting at the airport. The airport was double to triple per day what Aulani charged. Maybe find out who the PP got their deal through.