Agree with President Jim. Request the bylaws again. Go to the Principal. Go to the superintendent.
Having last minute (secretive) meetings & elections is a cause for concern. As parents, you are supporting their fundraisers with your money, but there doesn't seem to be a means to find out details of the spending of those funds.
Parents are supposed to be involved with their childs education & school events. They cannot just "use you" when they need you and then cast you off other times of the year.
The bylaws would determine if the 2 without children in the school even have a right to be there. When a person won't "give up the ghost" and move on, there are usually issues. Why they wouldn't run at their child's new school, but hold a position where they don't have a vested interest seems very strange, to say the least.
Keep trying and assert your right as a parent, a PTO member, and supporter of the PTO. Also, you may find others that feel the same way you do or would if they knew what you explained here. Frankly, if I got nowhere, I'm not sure that I would support any fundraisers of the PTO. I wouldn't know if the money was being spent on school programs or their hair & nail appointment!
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One possibility is to start your own group. If you are that sure that there is no way to work this out, you can start a similar, yet different group. You would want to run this by your Principal, but with the issue you explain I can't see why he would have that much of a problem with it. It's all for the betterment of the school and the kids.
Maybe before you get to this point though you may want to push for the Bylaws with the Principal. The group should have one and then depending on what they state there may be other avenues that you can pursue.
If the Principal is unwilling to help you you may need to take it to the Superintendant of School, effectively the Principal's boss. Maybe mention this to the Principal first and explain that you feel that it needs to go to that level as you aren't getting the results that you are looking for. It seems that in response to his "Nobody ever wants to help" you explained that you did. What happened then, how was it left. Not sure if this was a scheduled meeting or just a quick question in the hall, but you may wish to schedule an appointment with him and all three of the members that you are talking about. See how that works out and let us know.
I ran for a pto office at my school. In each office was 1 new person and the other one has held the office for at least two years. None of the new people got voted in. They scheduled the meeting the day before at 9:00 am knowing it would be hard for parents to get there. Then took ballots around to teachers waiting for them to cast there vote. The only people at the meeting were three of original officers and three of the for running for an office. The president wasn't even there. 2 of the officers do not even have children in the school but will not give up there position to new parents who want to be involved. This was actually the first pto meeting i have ever heard about and my child is in 3rd grade. I have asked about bi laws and i get ????looks. So i am searching for advice in what is my next step. Ihave talked to the principal and i get nobody ever wants to help. My response is there are alot of parents that want to help that i have talked to personally but are not given the chance to. I don't care if i have an office i would just like to be involved.