As a president of an Elementary PTO I'm surprised about a few things. First, as others commented, that your Bylaws state that the Principal can fill open board positions. That is a problem to begin with and I would look at having the Bylaws reworded.
Also I always promote the fact that EVERY parent, guardian or staff member is automatically a member of the PTO and are encouraged to become active. This member seems like an ideal parent. She seems enthusiastic, energetic and will get things done. She just needs to be shown the way, and that is your job.
Now I know that you have tried to explain to her that what she is doing is not her job, because she is not a board member, but there has to be a better way to handle this. Do you really want to lose her? Why not try to make her a welcome part of your committee, instead of the overzelous outsider that she presently is. Now, at least in the PTO I am involved in, someone can be a coordinator of something without being a member of the Executive Board. Why not try to give her something where she can focus her energy?
You wrote:
"I told her that once again she is not on the board and she does not need to be calling parents to volunteer that that was my job."
This is also surprising to me. It may be due to the size of the school, etc., but I have a specific position for obtaininv volunteers that are needed for various functions. This position is called "Volunteer Coordinator". As President I am way to busy to have to be coordinating volunteers for all of the events and programs that we run. So why not give her that role? Make her the Volunteer Coordinator. It sounds as though she would be a great resource. She would probably always have enough volunteers, be there to help coordinate if needed and likely even send out thank you letters, which would make for an ideal Volunteer Coordinator.
Now my PTO has a rule that anything that gets sent home needs to have my (the President's) and the Principal's approvals first, and you can enforce this with her.
I don't mean to assume, but there does seem to be a little bit of an underlying theme that she is "stealing" some of you responsibility, but it doesn;t have to be that way. Truth is, I commend you on being so honest about this person, because you do paint her out to be a perfect active member of the committee, she's just overstepping her present bounds. I would say it's your job to not lose her and not offend her. Make her part of your group and I think you'll be happy with the end product.
-Jim