BTW, I have an aunt who had a falling out with her parents (my grandparents). They remained estranged for 25 years until my grandmother was dying and my aunt was in foreclosure. My aunt then saw my grandmother right before she died. But, my grandfather and aunt then immediately went back on the outs until his death.
This fracture in her family had and continues to have horrible effects on her children. They are pretty messed up by it.
Your children already have to deal with having two separate families, your family and XH's family. Ideally, these two separate families could peacefully coexist, independently, each being a safe space in their lives.
But, right now, no matter what you do, this can't happen for you kids. To have such significant and public infighting, judgment, lack of compassion or forgiveness within XH's family that maintains a painful fracture is not good for them.
Look at it this way, you understand how it is bad for them to be in a place where they have to reject/hate GF to be loyal to you. You don't want them to be in that place. You have tried to help them not be in that place, and I think you've probably been doing a great job with that. But, meanwhile, your ex-in-laws take the kids right back there. They can't be loyal to their grandparents and accept GF at the same time. They either have to reject what amounts to their father's household family or their grandparents. It is messed up, and very sad.
Your ex-in-laws are rejecting their child because he had an affair. Affairs are wrong, certainly. So are lots of other things. They are forgivable. I hope your ex-in-laws are able to extend some compassion to their son and his significant other, sooner rather than later, so that your children don't continue to be put in the middle.
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And, help me out here. I'm really concerned that you used the phrase "push my buttons." I'm not sure what to make of it. It sounds hostile to me, like you think I try to prick you for fun or something. Is this really how you are feeling or am I misreading that?