Is father of children allowed to take them out of state for an extended period of time without mother consent in state of Virginia?

In the absence of a court order, there are no rules in place governing the terms and conditions of your custodial arrangement.  Further, if the court has not addressed these issues, you don't have any legal basis to seek enforcement.  Lawyers.com offers general information and not legal advice.  Therefore, in order to protect your rights and the interest of your children, I suggest that you consult with a lawyer in your areas to discuss this matter in greater detail and obtain advice on what is necessary to discuss options, including return of the children.  Lawyers charge by the hour for consultations, therefore, you should be in a position to discuss fees in advance of setting up a meeting, to avoid any misunderstandings.  Best of luck ~