For some reason, it seems even worse that she's "officially" advocating for the firing of the deputy national security advisor. Nancy not only knew not to issue any press releases, but she went for arguably the biggest game in the person of the President's chief of staff.
Of course, going after anybody on the basis of personal animus (almost certainly the case here) is just plain wrong. At the end of the day, the idea behind giving the President's spouse special status and funding is that s/he will support the President, and the agenda of the first spouse will not interfere with the workings of the rest of the government.