I totally agree with EaglePrez...Get those BY-laws in order but aside from that, you can force her hand if done correctly.
We are having a conflict with our by-laws this year as well and (since my resignation as Prez in January) I have watched my successors do little to improve the school or the PTO. They have done very little for the students this year and praise themselves CONSTANTLY for a job well done. I don't see it.
As for our elections (held every Spring) the seated board members are choosing which portion of the current By-laws they want to adhere to in the subject of an election. The general membership who is already outraged at how little this group had done for our students and the traditiona that they have put an end to, have formed a Quorum against them and have been passing around petitions to force these Officers to follow the rules and play fair.
You might try starting your own petition and getting the majority of the General Membership to sign it calling for a Special meeting to discuss the topic of elections.
Since there are no current by-laws in place, then there should be no set date to hold and election there by living it up to a vote of the general membership. You might also use that special meeting to vote in some by-laws or at least pass out a copy of some to the membership and vote whether or not to accept them at the next meeting or the First one of the school new school year.
Good Luck and hang tight, You'll regret quitting and leaving it all up to her. I do.
Jill