Wow, I'm really surprised by your responses...Our principle did inform our PTO that the picnic will remain the same in the future, no chance of ever changing. When we did meet and accepted the fact we were going to be forced to participate, we told him we would not be doing the picnic next year at the same location. I guess from our perspective, he doesn't have the right to tell us where to spend the money we raise. He agreed to allow us to take the kids to the camp and then did an about face. The other schools PTO took their entire school on a trip to the zoo. That is where they decided to spend their money. We decided to invest in smartboards for every classroom..at a cost of $22,000...we have raised in the past 3 months $7,000. I am concerned that when the parents who volunteer their time and money find out about this, it will be an issue in the future.

CC's right. Unfortunately these boards are filled with small people doing small things and usually what really kills them is when the big people continue to ensure the kids interests are put above the pettiness. Perhaps this is the last time for this particular tradition unless there are some accommodations made by the 2d group. It may also be constructive to organize a meeting in advance, with written notice to the other group and principal (and whomever else is necessary to attend) and make the agenda about the location of next year's picnic (if there is to be one). That way everyone knows there is a meeting, if the other side doesn't show then you make decisions without them.
As to this year, appear gracious and enjoy the picnic. The kids will be better for your approach.
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Without knowing you or any more details than the ones provided in your post, I respectfully offer my opinion that your PTO pay for the trip and graciously meet the other school at the original location. And by graciously, I mean graciously....

Unfortunately, this other PTO didn't appear to play nice. A handful of adults used what power they had to manipulate a situation to their favor. It happens all the time. Really, all the time! Their pettiness will come back to haunt them some day.

What you, your group and the rest of your 4th grade teachers, parents and students can do is go to the picnic and have a fabulous time. That's what it's all about anyway, right?

I do understand your frustration. It's bad enough that this powerful little group of four to six people has absolute control over their own PTO and school but now, seemingly, over your's too for this one event. I have to agree with your principal though. Kids learn all kinds of things at school and only a portion of it is from the curriculum. They learn oh so much more from the society around them. If they see you promoting positive interactions with the other school, you are giving them a great gift.

I'm going to try to give the abbreviated story. Our town has two elementary schools that go up to 4th grade. Each yr. both elementary schools get their 4th graders together for a picnic which is funded by the PTO's. Early into the school year, our PTO decided to try to change the location of the picnic due to input from parents/students. We reached out to the other schools PTO's President in February to try to meet with them to go over other options and suggested a local campground alternative. Even though they are 501(3)c, they do not hold any meetings. The executive board does everything themselves. Bottom line, they put us off for months and refused to meet with us and then lied to their principle saying we sprung this on them last minute. They booked the regular site and got the trip approved by our school board without our consent or knowledge. When we approached our principle and explained what happened, we were told we had to fund the picnic anyway. We requested a meeting with our schools principle. At the meeting, it was mentioned that the principle couldn't tell us where to spend the money we raised as we are a non-profit org and that we weren't going to pay for the picnic. Finally, it was agreed that we would fund the 4th grade picnic as long as we could take our 4th graders to the campground on a separate outing. While I was out of town, the principle called a meeting with the PTO and told them the trip to the campground was off and he still expected us to fund the picnic. Any suggestions on how to deal with this situation? We've had a pretty good relationship with the principle up to this point...but we've never had a disagreement before either...