Um...no can't say I ever have. Sounds like a very embarrassing exchange and I hope that my own PTO never gets to a point where something like this happens. I suspect there's enough blame to go around and so I'll save my "playing nice with others" comments for a dear abby letter.
As to the question of your removal, you need to look at your bylaws. If there are provisions in the bylaws for the removal of a member for behavior unbecoming or in opposition to good order and discipline of the PTO, or whatever circumstance, then your PTO must follow them to "legally" remove you from your position (which I would suspect involves a 2/3 majority vote of a quorum present at another meeting). If there are no provisions, and there is no way to remove a parent, then I don't think they can just "stop letting you play". As to you making things better with the family that you had the exchange with, that may have no impact on the PTOs decision to press you for removal, especially as a board VP. That's one of those positions that demands all the grown up aspects of leadership.
So if you were removed legally, according to the bylaws, you may request reconsideration. If you were removed illegally, then you're not removed. But I suspect any authority you have is severly degraded.

Okay so let me explain the situation. There was a meeting last week there are and entire 8 of us on PTO together. One of the children came into the meeting crying because she was being picked on (i might add that this happens almost every meeting and not to the same child.) she then went out to play with the kids again. She came back into the meeting about 30 minutes later and had gum stuck in her hair and was crying because of it and she fell. Well needless to say my daughter was one of the girls who was not being nice. The childs mother called her father and he came to pick her up. He was upset and told my daughter and another girl that if "they every pick on his daughter again they will get beat up and have all thier hair pulled out." (well he said something to that effect you know used some not so nice words and spead off the school grounds.) Upon hearing what the father said to my daughter i entered the PTO meeting picked up my stuff and stated that "if her husband every threatend my daughter i would have the police involed" (yes i yelled and did swear.) The mother then came back at me and said that my daughter called her daughter a loser. I then told her that "she is a loser" and walked out of the meeting. Believe me this has never happend before. I was reacting to my daughter being threatend. (oh yeah did i mention i was just voted in as co-pres. a few weeks ago). As for that mother and i we have apologized to each other and are fine now. PTO however not even knowing why i was so angry met with the Principal of our school and determined that i should be removed from PTO. I am embarrassed, upset, hurt and anything else you can think of. I have been involved in PTO for 2 years, I do box tops, cambells labels, help will all events, now do Sox tops and started a yearbook for 2006-2007. They removed me from my co-Pres position but told me that i could still do everything else. Is there some sort of by-law that i broke? They did not even want to hear my reasoning for such a outburst. I mean if that mother, father and i can make ammends and apologize what is the reasoning for my ousting. Please let me know how you feel. I must have cried for three hours, i love PTO i do all i can, believe me i have helped on everything and gone above and beyond. that would be why i was voted in as co-pres. Help I feel like i was personally attacked and don't feel i should have been removed from my position because of my outburst.
Have any of you delt with a situation like this before?