Tertiary Education, payments direct to child

My ex and I divorced in 2007 and since that time, she has denied me access to my Son. My Daughter, who has endeared abusive situations from her mother to visit me, has now left home and gone to University, she is 19. Our agreement states that I shall pay child maintenance until each child reaches 17 or ceases tertiary education. (I pay spousal maintenance as well. )
Going forward, since my daughter is away at Uni, I would like to pay her directly as she has now taken on student loans in her name and I do not want her to leave school with large financial debt.
My ex is claiming that by not paying her, she will not be able to purchase a new home she was hoping to get later this year. (I don't know what responsible mortgage company would base monthly income on child maintenance when the children are 16 and 19!) Anyway, she is threatening to take me back to court to argue that she needs the monies to support the purchase of this home.
Does she have a case (and as background, she had full possession of our marital home and recently sold it and got the full proceeds). I left the marriage with no assets.
Please help.

The courts have taken the view that it isn't unreasonable to provide a base with the parent with the majority of care for over 18s in education even if they don't live there full time.

Unless you seek a variation you are in breach of a court order if you don't pay the maintenance when the order states that periodic payments should be made to the parent for the benefit of the child until end tertiary education.

However, seeking a variation may cost more than than the actual maintenance you are due to pay and even if you represent yourself you risk being ordered to pay the other side's costs if your application is unsuccessful.

Thanks for your quick reply. Is there a variance that can be granted that states that at least 50 % of the child maintenance that is paid should go direct to the child from the mother? The daughter is requesting money to 'live' on, for food, etc, we just want this to come form the money we pay her Mom. To this ponit, the mother is giving her nothing.
When does tertiary education end? First degree, etc?