I am from a small town and a small school. What few volunteers we have get along. We have never had a war at a meeting, though it was once rumored (I was just a member and I didn't understand the rumor everything seemed fine to me).
I considered doing a Conflict Resolution Training. Our sub teachers are required to do this, but since there was lack of interest I didn't do it. If there were conflicts that I was aware of I would have pushed for it. Your conselors probably have this info.
As for rewarding students that is something our PTO takes pride in. Before the Fall Festival one of our valued volunteers ordered crafts and we had the students to make them to sell at the Fall Festival. Most of them wanted to buy their own. I worried about this, even though they were a dollar I knew it wouldn't be possible for every one to buy one. So I really stressed that if they couldn't buy one they would be helping out our school just as much by letting someone else have the opportunity to buy their craft.
We have "Sucess Celebration" every Friday ( this was the principals idea). It recognizes academics and attendance. Every child eventually gets recognized. Some teachers get creative and give awards such as "the Neat Nelly Award".
Our teachers are great, our principal is very cooperitive, I hope you have the same luck.
If you decide to do the VP thing maybe you can work on improving your volunteer program, if you have some parents that don't work well together, I am sure you can find them some seperate but equally important jobs.
I AM THINKING OF RUNNING FOR VICE PRESIDENT AT OUR PTO I WOULD LIKE TO MAKE A DIFFRENCE AND TRY TO GET EVERYONE TO WORK TOGETHER FOR THE CHILDREN I KNOW IT WILL BE IMPOSSIBLE TO GET EVERYONE TO GET ALONG BUT I WOULD LIKE SOME IDEAS OF HOW TO MAKE A DIFFRENCE AND DIFFRENT IDEAS THAT WE COULD DO FOR TEACHERS AND STUDENTS, MAYBE DIFFRENT THINGS FOR STUDENTS TO DO AND REWARD THEM FOR LET THE CHILDREN HAVE A GOAL AND WANT TO WORK TOWARDS IT AND MAKE THEM FEEL GOOD ABOUT THEMSELVES BECAUSE LETS FACE IT NOT EVERY CHILD GETS PRAISED FOR EVERYTHING THEY DO WHETHER THEY TRIED THEIR BEST OR NOT THERE ARE THE CHILDREN THAT LOOK FORWARD TO SCHOOL BECAUSE MAYBE THAT IS ALL THEY HAVE AND THAT IS A SAFE PLACE FOR THEM. I JUST WANT TO DO A GOOD JOB AND TRY TO MAKE DIFFRENCE IF I CAN. IF I CAN HELP ONE STUDENT OR A TEACHER FEEL GREAT ABOUT THEMSELF THEN THAT WOULD BE GREAT.