Is the court ever allowed to prevent visitation without a hearing or evidence that the children are in any harm?
I am not licensed to practice law in your state. Therefore, I cannot inform you as to the specific laws of your state and can only provide you with general information regarding your situation.
Custody and visitation procedural rules are very state specific. Most states do permit the courts to enter temporary orders based on the best interest of the child(ren) or the health, safety and welfare of the child(ren) based on limited evidence.
That being said, usually a full evidentiary hearing will be held before the court enters a permanent order regarding the custody or visitation of a child. In Virginia, where I practice, the courts rarely will enter an order based on an ex-parte motion unless it is an extreme circumstance and the court believes that it is absolutely necessary for the protection of a party. But even then, most judges will place the matter on their docket for a full evidentiary hearing on the matter shortly thereafter.
It would be advisable to find a licensed attorney in your state to sit down with and to discuss your options as well as what you can expect procedurally from the court system in your area.