It's not strictly a MIL issue. It's a broken relationship issue that just happens to be your MIL.
I think she is unreasonable, but who is ever reasonable after a break-up. Even if she initiated it, FIL had been a part of her life for a long time, and he is moving on. It hurts, regardless of the circumstances.
You didn't do anything wrong, but she isn't in a place to hear it. I would step back a bit personally, let your DH deal with her for a while and see how things go.