Do not take revenge, my dear friends, but leave room for God’s wrath, for it is written: "It is mine to avenge; I will repay,"
That’s the verse your user-name refers to.
So I wonder how you could approach this situation in a way that could be supportive to your wife, her extended family and your marriage.
I generally believe in total honesty. I can imagine you and your wife agreeing on some statements like:
"We are working at reconciling our marriage. We might not be 100% certain how we will do that or if it’s possible, but for now we are trying. One thing we can agree on is that our mutual infidelities are part of our problem and something we need to deal with. Part of dealing with that is that neither of us interact in any way or form with any of our former affair partners. If interaction happens, we minimize damage by getting out of that situation and sharing with the other. This is mutual, and is agreed on by us both as something required in order for us to possibly reconcile."
Frankly – if she can’t agree with the above then you two aren’t in reconciliation.
Second statement:
"We can agree that it can be important to have a good relationship with close family, like your sister and BIL. I realize they received you once during a difficult time in our marriage, and I should appreciate they took care of you. I do however have an issue with their friendship with OM, and we need to find ways to mitigate that concern."
Third statement is one you agree on and present to SIL and BIL:
"We appreciate your friendship and your assistance to our marriage in these difficult times. We are working at reconciling and think it would benefit us to be able to have you in our lives. However we do NOT want to interact in any way or form with OM. We ask that you ensure that when we are with you (either singularly or as a couple) that you do not talk about OM, events OM is at or accept him to your presence when we are there. It is imperative for our marriage that neither one of us interacts with OM. What you do outside of that is not our concern. We appreciate your help and compliance on this issue".
If you two can agree on all three statements (or more appropriate versions for you) then you two as a couple have a good chance to reconcile. Her family can react in a couple of ways:
They can tell you and your wife that you two do not control their social life and refuse to take your wishes into consideration. To me I would view that in a comparable way as I would friends who might refuse to not serve peanuts due to my peanut allergy (just a simile – love peanuts!). I would see this as a clear sign that they aren’t positive for the marriage.
They can accept the statement, but largely/partially ignore it. Might ask you over for dinner and talk about OM and work, might have a party and he’s there serving the drinks or whatever. That too should be a sign, and since the sign is the emotional equivalent of a full-size billboard your wife will recognize that they are NOT helping.
They can be supportive and agree to your statement and respect it.
"If, therefore, any be unhappy, let him remember that he is unhappy by reason of himself alone." Epictetus