The Beginning With Children Charter School, housed in a former factory in Brooklyn, N.Y.,landed on the state’s list of high-performing schools this year. But its founders and wealthy patrons, Joseph H. and Carol F. Reich, think it could be better. So last month, the couple forced most of the school’s trustees to resign in a push for wide management changes and better student achievement. The clash has exposed fault lines of wealth and class that are perhaps inevitable as philanthropists increasingly invest in public education.