Well she has mental issues. Mentally ill.
You cannot fix her... she WILL twist anything and everything around, making it awful. No matter what.
A "relationship" with someone like this, is not possible. Because they do NOT have the ability to rationally understand "normal" behaviors or relationships, nor own up to any wrong doing they are committing.
Thus, you have to, detach yourself... and realize, that when you are dealing with her, you/Hubby are dealing with a mentally warped person.... who is not dealing with normal cognizance.
If you continue to take it personally, and try to have a relationship with her, making her "normal" it will not work... and it will cause MUCH strain and problems and burdens upon you too, mentally and emotionally. People like your SIL, have a way of dragging down others, and making THEM mentally strained too.
So, you have a choice. To try and fix her and have a relationship with her or not.
Neither is easy... since SIL has involved the entire family and poisons them, too.
She is Toxic... and toxic people will make others poisoned too.
My friend, has a MIL like that. After years of trying to have a relationship with her and getting along for "family" sake... she and her Husband "disowned" her. Only then, have they been able to have a normal life... without being poisoned by her MIL. Her MIL caused sooooooo many problems... and is pretty much mentally ill and mean and just NOT able to change. They are much happier now. Her MIL.... not even her neighbors or Husband like her. Everyone just put up with her... because they didnt' want "problems" from her... so they just gave in. And even if they gave in and catered to her... it was NEVER enough. She would always conjure up more problems or faults, or criticisms, or issues. Imagined or not. But it was never "her" fault... it was always my friend's fault... being the Daughter-in-law... and her Husband (MIL's son).
People like this, will not stop. So know that.
Unless a professional Therapist is seen, by your SIL.... she will not change. Or... she will continue to cause you/Hubby problems... and then YOU and Hubby will need to see a Therapist, because of her and the stress/hardship/problems/marital problems, she causes you and your nuclear family.
Either EVERYONE in the family (yours and your Husband's) STOP putting up with her and puts her in her place.... or, it will not work, and she will continue her vendettas. Because if only you/Hubby try to change her or "Correct" her... it will not work.... because she will just infect the other family members and make up stories about you, still. So, unless EVERYONE stops her and refuses to put up with her... the toxic person, will still be "able" to continue their menacing, upon you.
All the best,
Susan