I would do everything that you can to prevent this. If it happens you'll be effectively creating two PTA's, with separate goals. Thia is not good business.
As President I would talk with everyone in this committee separately, and then as a whole explaining that the school has one PTA and that you need to resolve the situation for the children's sake. If it is legitimate that all of the the volunteers won't work with this one other person, then you'll need to talk with that indiviual and make some changes. Not sure of the specifics regarding this, but I might ask the chair what she would consider as a minimum to be resolution. It may be that that person is not on the committee, or maybe something (hopefully not) more.
ACK! In the midst of personality conflicts, a current committee chair has asked that the board consider allowing it to remove itself from under PTA. They want to be a stand-alone entity doing their own fundraising, etc. This is an admitted effort to avoid dealing with another volunteer.
I have suggested that a neutral person be the committee chair with all discussion flowing thru the chair, but I'm told that the entire committee (all good volunteers) doesn't want to deal with this specific volunteer.
I'm very upset by this - a committee seceding from pta - who has ever heard of that?