A sweep is more than a forced move. It is a police presence forcing the people out of the park/encampment, usually without advance notice, followed by a clean up that involves throwing out everything that the people there couldn't gather up fast enough and carry when being herded out. Sweeps strip the homeless of their few possessions, particularly of tents, tarps, sleeping mats, and whatever other makeshift shelter they might have set up, while doing nothing to solve the actual problem of homelessness. They're just left to start over, still homeless and now homeless with nothing but the clothes on their backs. I can completely understand why the school board would want to see more humane means used to relocate the homeless people living in that camp.
It's not a campground it's school grounds. Their stuff (all that stuff you mentioned PLUS their feces, needles and filth) don't belong there. If school is in session all of it needs to be gone one way or another.
Would you want your children to have to walk through that encampment or what's left behind. Would you want them to be playing outside for recess and stepping in human waste, or finding a used needle?
The kids deserve humane treatment as well and since it's their school they come first IMO. The homeless camp should have never been allowed there in the first place but since it was and school is in session it needs to be sweeped if the people are not willing to leave on their own.