Wealthy parents （主语）have always been willing to spend （谓语动词）the vast amount of extra money （宾语）necessary to send their children to schools with a perceived educational edge.（extra money 的定语）

with a perceived educational edge 是 schools 的定语。

既然 necessary 短语是定语，可理解为 money which is ecessary to send...

necessary 的一个特殊用法是：Sth. is necessary to do... （某物对于作某事是必要的）。例如：

The government has reaffirmed that it will take any steps necessary to maintain law and order. 

政府重申将采取一切必要措施维护法律和秩序。

《柯林斯高阶英汉双解学习词典》

We will do whatever is necessary to stop them.  

我们要采取一切必要措施去阻止他们。

来自柯林斯例句

The United States will do that which is necessary to meet its obligations to its own citizens 

美国将为自己的公民尽其应尽的义务。

《柯林斯高阶英汉双解学习词典》