I have a different take on this.
My husband's family is on the East coast (we're on the West) and he doesn't have a very close connection with them. So when I was having my affairs, he went to my family for support. It drove a wedge between my family and I that still has not been removed. The relationship I have with them is now very distant and "casual". That being said, they have stronger connection with my husband.
I would just point out that this is a consequence of your affair. If there is a wedge, it is due to
YOUR ACTIONS, not his. If he has exposed that you were singing too loud in church, there would be no wedge. If my sister had an affair,
her AFFAIR would drive a wedge between us because I don't consort with adulterers. Now, if she changed and repented, I might befriend her again, but she would have to work to remove that wedge.
In fact, my sister is a druggie and THAT has driven a wedge between us. I told her when she is ready to straighten out, I will be there to help but I don't associate with druggies, sister or not. So please, lets not blame the TELLING of the truth, when it was the SUBJECT of the truth that drove the wedge.
Monc, please listen to Dr. Harley and other posters who are in recovered marriages. Your FIL is more concerned about protecting his DD from the consequences of her affair than he is in helping you save your marriage. He does not know how to save marriages.
Exposure is bound to make some angry. Mostly those who are corrupt themselves. But folks who know right from wrong will stand on the side of your marriage and will not throw you under the bus for exposure.
Exposure is simply the most powerful tool you have at your disposal. It is like chemotherapy to cancer, REGARDLESS of whether the foggy minded and those with an agenda object.
Do what is right and stop listening to the chatterers and the naysayers who don't have a CLUE what they are talking about.
Man up and do it because it is RIGHT, and ignore your FIL. Tell him "thank you, Sir, but I choose to follow the advice of a PSYCHOLOGIST who knows how to save marriages. I know you love your DD and want to protect her from conflict, but I also love her and intend on doing what is right for my marriage. I hope you will support me in that endeavor."
Dr. Willard Harley, clinical psychologist and author of Surviving an Affair:"I'm in the process of rewriting "Surviving an Affair" to add information about plan B. Some of the main points are as follows:
Whether in plan A or B, the world should know about your husband's affair. All of your relatives, your friends, your children, and the licensing board for your husband's lover. In some states a licensing board will revoke a license if a counselor is having an affair with a married person, client or not. This is because it's well known that affairs hurt families, especially children. And counselors know better than to have an affair.
The reason for the wide exposure is not to hurt the unfaithful spouse, but rather to end the fantasy. Your husband's secret second life made his affair possible, and the more you can to to make it public, the easier it is for him to see the damage he's doing. Keeping it secret does damage, but few know about it. Making it public helps everyone, including the unfaithful spouse and lover, see the affair for what it really is.
<snip unrelated>
When I first started recommending openness about an affair, I wasn't sure what would happen. But I did it because I knew it was the right thing to do.
Now I know that for most couples it marks the beginning of recovery." 
