I'm not going to apologize to my brother in law's inlaws
Why don't you want to apologize?
They are mocking me behind my back. I don't want to give them the satisfaction of an apology
If you have done something bad then the thing that most people would respect would be for you to own up to it and apologize.
I haven't done anything wrong, I'm a good son in law.
You might feel like you haven't done anything wrong, but they may feel differently. It's best to just apologize to them and move on don't you think?