It wasn't illegal under D.C. law since that only requires the approval of one of the parties being taped. But taping a conversation in a secure area like the Situation Room? I would not be surprised if that didn't violate some federal law.
You’re on the right track. The White House Situation room is a SCIF - and a VERY sensitive one at that. Sneaking in and using recording devices is not your run of the mill security violation. It is Espionage under 18 U.S. Code Chapter 37. Further, President Trump issued new Non-disclosure edicts, which all WH personnel signed. Legally, she’s screwed - if the White House has the politically will to pursue the case.