sorry guys, but this doesn't pass the sniff test with me.
to clarify-- your spouse cheated on you with a classmate. then, other classmates became aware of the situation. then, your spouse's paramour went all "fatal attraction" and is now wanting to ruin the career of your spouse? in all the scenarios i've been privy to, this would be the first where the paramour attempts to destroy the person they were sleeping with. what makes even less sense is the reason you give behind it-- that they are going after your spouse because classmates found out?
what is far more common? you, the OP, find out your military spouse is cheating and go after him/her with guns blazing. or, go after the military affiliated paramour with guns blazing. or, if they are both military, both.
i'm not saying your scenario is impossible, but it is one of the oddest jerry springer-esque situations i've been privy to. maybe this person really is bat**** crazy, in which case i would just ignore them unless they make specific threats. freedom of speech means a lot, and slander/libel is only applicable if the person knowingly is lying. if they really believe it to be true (and if it is true) nothing you can do can change who they talk to.
if my spidey sense is correct and you are fishing to see if you can do anything to an HPSP spouse for cheating, the answer is not really. a civilian "petitioning" the military for something works about as well as the military telling a civilian what to do. is there a slim chance it may stick and affect his/her career? maybe. but the burden of proof is probably large and most commands wouldn't touch this with a ten foot pole. they rarely do anything to blatant violations, let alone something like this.
finally-- protecting assets and everything is good, but if you don't have kids and this is a big trust breaker/deal breaker, a clean split is not a failure. you likely don't have that many assets to split and you have a lot ot life ahead of you. speaking from experience, divorces suck and have many layers of pain and misery but can also be a time for some self reflection and may end up being one of the better decisions you make.
good luck, and i'm sorry to hear about your situation and hope things work our for the better.
--your friendly neighborhood blended family caveman