Legal Question in Family Law in Kentucky

What you are asking about actually is "custody" rather than "rights". A custody agreement can divide up decision making authority anyway the parents wish. It can, for example, give all educational decision making to the mother and all medical care decision making to the father. So, the answer is yes. Giving up an aspect of custody does not deprive you of your rights. So, if the parent with educational decision making is doing something with that authority that is harmful to the child, the other parent still has the right to bring the matter back before the court.

One cannot give up a single "right", though. You either have parental rights or you do not. If you do not have rights, then you would not have the right to take the matter back before the court.