Hi, Lily:
This case sounds very strage. From finantial point of view, every organization is trying to save money. To add an un-necessarily big management layer sounds like to burn out money un-necessarily. You can say your director is crazy, but she must be doing so with support from her boss. So I am guessing maybe there is something else going on. Otherwise it is weird that your director can get the greenlight to do what every one else thinks not smart.
At this time, I think you can either ask the question, or just wait to see what else might come out.
Just my 2 cents...