You should have received a letter from centrelink stating that you are elligable for CCB, what hours and what rate if you have been assessed. Take that to the centre. If you don't have this letter, then someone at centrelink hasn't processed your request. I am a director, and this happens alot, centrelink tell families over the phone that all is set up, yet when the centre tries to enrol the child, the enrolement won't process because it hasn't been.
A little background to better help you understand - when a child enrols at a centre, we must have both the correct family and child CRN, and correct parent (depends if mum or dad registered originally which parent) and child date of birth. The parent will also need to have been assessed for CCB elligability and that to have been processed. Otherwise, when we hit the enrol child button, all we get is details incorrect, invalid or not found.
From a centres point of view, we have to charge you full price until this works, as we have no way of knowing whether you will ever be elligable for CCB and can't risk being left with a big bill - as has happened to many a centre in the past.
Call centrelink again, tell them your issue, ask to speak to a supervisor and get a receipt number for your call. The centre can then ring if they are still having issues and provide that receipt number and get it sorted out. I had to do this with one parent who was having the exact issue you are, being told one thing when it was never being done.