Greeting from a fellow New Jersian, who has also been betrayed, and kept the secret for way, way too long. But if it is any comfort, exposure is your choice---so you have to option to disclose or keep it a secret. While I definitely believe in informing the other betrayed spouse, you may have your own reasons not to disclose to friends and family. Your choice.
Did not disclosing to family cause affairs #2, 3, or whatever number? In my opinion---no. She cheated again...and will continue to do so...until she has the desire to put in the hard work to discover her root issues. While you can demand that she go to IC, it won't make a difference unless she wants to go.
Personally, with your current state of indifference, I would do (2) things:
First, please read, re-read, and re-read again yearsofpain25's posts. He really helps add the perspective from the childrens' viewpoint. Not that others here don't, but his story has really driven home how infidelity impacts the entire family....especially children.
The other point is to use your indifference to your healing advantage. Although you do not feel this way, you are at a point that many newly betrayed members strive to reach. We are often too paralyzed by fear in the early days to act in our best interests---and you are way beyond that point. Yet, you are not beyond the point of POSSIBLE reconciliation.
So, keep positioning yourself like you currently are doing. Inform family, if that is what you wish. See a lawyer, and learn your rights(my brother is divorcing after 30 years of marriage, and I agree with others that NJ can be terribly biased...although that is not always the case). But it definitely helps to gather knowledge.
All the while---WATCH YOUR WIFE. See if she is making wholesale changes, without your insistence. See if she can become the woman that you fell in love with years ago. Who knows---maybe she can turn it around. Maybe you still won't be interested. But with your indifference, you may have the choice to divorce or re-commit.
On a side note--after my last D-day, I was hellbent on divorce. No one was going to stop me. And I told my WW that she sure as hell better fix herself, because with or without me, she was going to have to be a productive mother and member of society.
And she did. Without my influence, because I was working on exit strategy, she dug deep, and found her old self. She was a good person for way longer than she was a bad one, and works hard to this day to keep herself in line. And I am still here....BY MY CHOICE.
I am not telling you to stay or go. Just to make the healthiest choice for YOU---because that is what your children will see and feel as they grow---a father who stood up for what was right.