Shared care shared responsibility. Ex wife not contributing to costly medical bills

[Cmacbstar]

Hello I hope someone can offer me some advice. I have shared care of my children. 50/50. My son got very sick in August while in my care. My ex wife and I were informed that there was a case of meningitis in his class. I took my son to the doctor and on arrival he was placed on oxygen and the doctor called the ambulance. Ambulance bill was sent to my ex wife’s address. It was ignored until now and has now been passed on the state debt recovery. On hand over of the children, she gave the nsw revenue to my son to give to me. Initially when I contacted her she said that she would pay half. Which I would assume with shared responsibility was a fair thing. She is now saying she isn’t paying because she did not authorise the ambulance ride. She has told me she has changed my sons address so the bill will now be sent to me. $846 dollars may not sound like a lot of money but it is for me. State debt recovery, on speaking with them today said they cannot split the bill. Is there anything I can do my concern is going forward what happens if kids need braces etc in the future can I just expect this to continue. Thank you any advice would be great