The only thing the evidence shows is a teacher filming her intercourse with her student of legal age, nothing more. In most colleges/universities the act itself isn't even illegal, it usually falls into a category like "conflicts of interest in the workplace" so the worst case scenario for the MC would be having to retake his gender studies course since his grade could've been compromised by favoritism. As for Jade, if B&R has a specific policy concerning such relationships she could potentially lose her job but there's no generally enforced rule against it and it's certainly not against the law.
It being a task on the pledge board could be a problem for the fraternity but at this point you're just assuming the MC or any other DIK would snitch about that. It's not mentioned in the video so there's absolutely no need to bring up that detail during the hearing about the incident.
Not sure how you meant "losing her children". Legally it makes no sense, they're too old for it to be a custody issue (certainly not for Tybalt, don't know about the age of the other kids). On a personal level, I'm sure Jade would drop the bomb about her husband's affairs, after that it's up to their judgement which parent they prefer in case of a divorce.
All in all, it's likely nowhere near as much of an issue as the game makes it out to be for the sake of drama. Besides, if it was as serious as you described we wouldn't have to worry about it at all since the revelation would basically end the game, meaning it won't be revealed.