Yes, a parent subject to a court order to pay child support is obligated to pay that support to the other parent. If the paying parent fails to pay, he may be brought before the court under a petition for contempt for failing to abide by the court's order. If the court finds the paying parent in willful (he had the ability and failed) contempt that parent can be jailed, sanctioned, fined and forced to pay the child support he has failed to pay.
Now, the court is not all-knowing, so usually the other parent has to file a petition alleging contempt for failure to pay child support. Otherwise, the court would normally have no way of knowing about the failure to pay. The court will schedule a hearing at which he has the burden to show he has paid the money he is accused of not paying. The very interesting thing about contempt for not paying child support is that it never goes away - ever. Even if you are 19, 20, 25, etc. if he has not paid, the other parent can still seek a finding of contempt for his failure to pay. Also, he cannot file bankruptcy to avoid paying what he owes.
Finally, your comment about paying your dues touches on the idea of paying support "in kind" (in other ways). I advise paying parents that in kind payments are very dangerous. The court will expect that the support be paid on time and in cash (or a cash form like a check or a direct deposit). If there is evidence (like an email or a letter) that the parents agreed that the in kind payment was in place of regular child support, that should be fine. If there is no such evidence, the court has some discretion to allow the in kind payment to suffice or not, hence the risk.
I hope this is helpful to you.
Essentially, your father is still obligated to make the child support payments based on the Court's Order. Your mother would need to institute a contempt petition in order to retrieve the unpaid support. In the event that your father and mother agreed, and upon a showing that there was an agreement, some courts are inclined to treat the payment of senior dues as support in kind. However, many courts will find that the payment of senior dues was merely a gift to the child and still require the payment of monthly support. I would advise that your mother contact myself or any other Family Law Attorney in Georgia for a more detailed evaluation of the facts in your case. Best of luck to your family!
Please note that this answer does not constitute legal advice, and should not be relied on since each situation is case specific. It is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.