If you cannot overcome your fear, then you should talk to your father immediately. It is the job of your parents to either reassure you or to work out an alternate arrangement. Your father should not insist just because it is his right to have visitation if it is not in your best interests to fly. This is a weighing process, because it is in your best interests to have visitation with your father.

Perhaps you can travel some other way. You do not say how old you are. Frankly, a minor unaccompanied by an adult is very likely to be safer on an airline than traveling by bus or train.

The judge will not read a letter written to him by your mother. This would be an ex parte communication, which means that it is only one side speaking to the judge. The judge is not supposed to listen to one side without the other side having a chance to speak.

If your mother simply does not put you on the plane, that is, if she disobeys the order for visitation, your father can file for a hearing, and ask the judge to punish her. Your mother and you will then go into court and tell the judge why you did not come. The judge will decide whether your mother's decision was in your best interests, or not. The judge also could rework the visitation schedule so that you did not have to fly.

This is not an easy matter. Good luck.