Does your pto require membership? If so, has she paid her membership dues, if not then she is not entitled to organize, handle money, and actually has no say, etc., but she would be able to volunteer. Also, if she is on the executive board, what does your bylaws say about removal of board members? Ours states "With a majority vote among board members, members may request resignment". Also, our parents that handle money has to be bonded - bond the ones you can count on and trust and do not bond her, and let her know only members that are bonded are able to handle funds. This has worked for us for the past 3 or 4 years. Also, if everyone ignores her, she may get the jest and quit on her own. You may politely ask her to control herself, because this is an image that is protrayed on the school.
I can't see you preventing her from helping at this point. But that doesn't mean to say that the concerns can not be taken into account. I believe that it should be up to the fundraiser coordinators to ensure that this one person is never put into a position where they can cause issues. If she will be in charge of money at some point, make sure there is a second person there for accountability. If she volunteers to be in charge of something that could cause issues, get a person to co-coordinate that with her, even if it is one of the fundraising coordinators. It's up to the President, and in this case, the function coordinators, to prevent this one person from causing any more problems.
Ok, so you know that this person is confrontational, you know she is mean spirited and vindictive. You know she is not trustworthy. You have all the other parents who work well with others shaking in their boots at the thought of having to work with this person again. What I am not getting here?
You need to do the politically incorrect thing and tell her that under no circumstances will her previous antics be tolerated. Period. Tell her that her reputation preceeds her and that it stops here. Period. Tell her that she will be allowed to participated but won't be be allowed access to any of the cash boxes. Period. Tell her that if she cannot accept these rules and play nice, then her participation is not required. Period.
Our PTO requires that at least on executive board member be present when money is collected and counted. This alleviates any concern regarding questionable collection processes. We always have two people working the cash box and run double tapes of the money at checkout.
As a PTO, you don't have enough grounds to not have her volunteer. Her personality aside, she is willing to help out. However, you CAN control in what capacity she volunteers. Have her coordinate the bakers and drop off of the products and then the set up. Ask to also see what community organizations will take any leftovers as a donation. But have another parent coordinate the volunteers that will work the table and control the money.
We have two parents like the one you described and we simply took the handling of money out of their control & responsibility. That way we knew the fundraising efforts were not going to be at risk.