Queen PTO, the first question I have to ask is about your bylaws. The fact that your group is a PTO would likely mean that you are an independant, non-profit organization. As such you should have a set of bylaws. My group's bylaws aren't the best by any means, but at least they provide some general guidelines. If you would like to take a look at my groups bylaws feel free to go to the website I created this year,
hill-roberts.kannoncom.com/ptoweb/,
and go to the Bylaws section.
So if you do have bylaws there should be some guidance regarding these types of problems.
Also I have to ask for clarification regarding your definition of "chair". Is the Treasurer or Secretary considered to be a chair or would they be given the term officer? My PTO has a meeting in May where we ask for members to step up for the following year. Officers and even event/program chairs are decided during that meeting. If I had an issue with a Chair not performing their "duties" properly, and I knew that they desired to keep the role, as President I would discuss the possibility of co-chairing with other specific members who may be interested. Then at the May meeting I would pass around a generated list and would have co-chair sign-up for those events/programs. That way you won't offend/lose the parent that is not meeting expectation and come next year procedures or necessary protocols will be followed/enforced because the co-chair will make sure.
Also who are the ones telling you you can't "fire" the volunteer? Is it the volunteers themselves, or your Officers, or possibly the Principal? If it's the volunteers themselves, then I would say that this has already been handled poorly. It should never have reached the point where you are asking for them to resign.
Overall this comes down to your President doing their job.
-Jim