I think your SIL is being a bit petty making jokes about it.
It could be that she’s just a bit of a bully, and your past behaviour makes you an easy target. But if that was the case, your MIL and your DH speaking to her about it would probably have made her back off, or at least only make digs when they couldn’t hear.
The thing is, you have shown yourself to be untrustworthy in interpersonal relationships.
She would be well within her rights to maintain distant civility or just have no contact with you. She doesn’t ever have to trust you, and that’s a direct consequence of your actions.
The jokes could well be her way of squaring the circle in a situation she’s uncomfortable with. The safety valve. She doesn’t want to have avoid family occasions, she does still love her brother/ his children and wants some contact with them. So she vents at you.
Whilst it’s true that your and your DH are equally culpable in the affair, there are some important differences between you vis-à-vis your SIL.
- Your DH is well, her brother. She doesn’t really get a choice over whether she loves him or not. He was in her life long before the affair, they are closely related. The roots of their relationship predate the affair by many years . With you, she didn’t know you/have a deep relationship with you before the affair. So the untrustworthy behaviour came right at the beginning of a family connection, poisoned the ground so to speak and your relationship never got a chance to develop.
- You’re a threat to her/to the wider family. Her brother is unlikely to run off with her partner, down to sexual preferences. You’ve demonstrated that you are no respecter of other people’s relationships. So she’ll never let her guard down with you. If there are other brothers/sisters as well this multiplies- to her mind you could go full Jeremy Kyle at some point and destabilise the family.
So it might just be sexism behind her treating her brother ok but you poorly. But it might not be.
I think she’s handling it poorly tbf, cool distance would be better than jibes. But I do get why she doesn’t like you, and that is on you. And also, I don’t know how you can overcome that or whether you should try to.
If you really can’t stand it, then you could try making a fuss, or going totally NC. But that could punish your MIL, or cause a bigger rift or mean your kids dion’t have a loving aunt in their lives. And it does reek of exactly the kind of selfishness that goes hand in hand with having an affair. No-one’s feelings matter but yours.