I agree with @99bottlesofkombucha
Im very sorry both you and your dh are in this situation. Its not helpful to attack your dh as he has grown up with this abuse and and may be finding it hard to accept that this is abuse (boiling frog syndrome) , just as serious as the other many kinds of abuse..... This has a whole new vocabulary list: triangulation, flying monkeys, grey rock, boiling frog and boundaries.
Speaking of boundaries: mil and Bil have said and done what they liked up to now, however upsetting, because there have been no consequences. Their life has not been made difficult in any way. This is where the boundaries come in that you set for yourselves in relation to his family. It took me a long time to understand boundaries.... Its not about you laying out rules and people have to follow them, as thats trying to control others which is impossible, its more about deciding what you will tolerate and what action you will take if you find that thing happening, usually when you have already told them once, for example.. From now on, if MIL makes false allegations about you or speaks derogatorily about you, she will not have contact with the children for x weeks. Having a plan in advance to help. Im hoping you and your DH will be able to work together to act as a single unit and decide on your boundaries.
Im not in the business of diagnosing anyone, and i dont want to offend anyone, but this kind of behaviour in my personal experience, is likely due to a non diagnosed personality disorder. The people i know, who are toxic, exactly like your MIL, have not been diagnosed. Please understand, we cannot EVER say, " i think you have a personality disorder", this will absolutely not work or help in any way. They are very unlikely to ever seek help or treatment. They lack self awareness. So in my case ive found Out of the Fog website very helpful. They have a section on boundaries. Also a reddit chat you could look for that i found helpful called "on boundaries with a little love for no contact". Also psych central https://psychcentral.com/relationships/tips-for-dealing-with-your-toxic-parents#tips
When you look into these websites and read enough stories, you will be amazed at the similarity of other people's stories so this is not that unusual sadly. Youve got a better chance of success if you and dh can work on this together with you helping him as it sounds like he is very much in the fog (fear, obligation, guilt).
I posted before on your thread, suggesting a letter very very carefully written. The reason for that is the tendency to twist what you say verbally into an outrageously warped version.....and then its chinese whispered round the wider family. If its in writing, it can still be twisted (it will be twisted, make no mistake) but you will never be gaslit or second guessing what you said so thoughtfully, politely and reasonably and carefully. You will have a record. This kind of twisting might not arise from malice. Its taken me 20 years, but Ive come to understand that its more that that persons brain puts a negative spin on something, they decide it means something else and basically reinvent and rewrite the facts in their own mind. They may never accept your truth.
My heart really goes out to you both and i hope you will find some help in the websites and articles i have suggested.