Overcharged $575.00 for baggage, despite a listed price on my ticket confirmation

On Oct. 22, 2018 we began our journey back to Canada. We began in Christchurch and we had booked our flight through United, but were put on a partner airline, JetStar. It was a horrible experience. We arrived at the airport early for our 6:30 am flight. We each had one checked bag, and then one ski bag making for a total of 3 bags. On our way from Canada we were charged 100$ for our extra checked bag. In Christchurch JetStar charged us $575 for our extra checked bag. We tried to explain that we had booked through United Airlines and showed the lady at the counter and the manager our United itinerary that had the baggage fees on it. The manager was unwilling to help us and refused to honour the United baggage policy. She told us to either leave our extra luggage behind or pay the fee. She was EXTREMELY rude and refused to even have a conversation about it with us. I cannot believe that United would partner with such a cheap, budget airline. We buy our tickets with United excepting a certain type of service. This is the exact reason we didn't go with a cheap, budget airline. We not only got charged an unbelievable amount for our extra bag, but it was not the way to start the morning or our over 24 hours of travel. We tried to complain/get a refund from all the customer service desks at each airport we stopped along the way and NO ONE could help us! I am completely unhappy with Jetstar. We travel all over the world and this was one of the worst experiences we have had.
Don't fly Jetstar!