Sounds to me as though M-in-law in a strange way likes being the poor mistreated wife and mother.
She had an inkling of the first affair and instead of confronting F-in-law, her husband, got her son to do it for her. Ask yourself...would you get someone else to confront your husband if you thought he was having an affair ? Don't you think you would do it yourself ? I'm sure she was very upset, but she's not doing much to sort it out and it is at the end of the day HER problem , not her son's and certainly not yours.
If she asks you or your husband to confront F-in-law again, I think , if you could , I'd tell her to take care of her own business. If you feel that you all absolutely must get involved in this, make sure she does her bit and doesn't just confine herself to weeping and having to be comforted.
It's very noble of your husband to want to protect his mother, but he really cannot continue to be their go-between. As you have already found out, despite what was presumably quite strong evidence (or else he would never have confronted his Dad) M-in-Law let it all get smoothed over and the only one who looked bad was ....your husband. I think your husband might appreciate your support NOT to get involved in this again. After all who wants to be used by one person in a relationship as a stick to beat the other one ?
As for your loss of respect for F-in -Law...that's gone and it won't come back. You have to just try to accept him for what he is, not hope that he will become again what you thought he was.
Your husband has a harder job with that , because he has to accept that his Dad is not a saint and someone to be looked up to, he's probably a bit of a cheat. Not only that, he's a bit of a cheat who was willing to make a fool of his son so that he could go on cheating.
Sorry to be so tough.
Good luck.