Your DH needs to handle this. He has to tell his family what is going on with SD so they understand. It's better he deals with his family and it come from him directly.

Build a framework of the facts so when SD plies her toxic bullshit, she will be spouting it to people who no longer are manipulation fodder for her crap.

Spreadsheet!  DH needs to keep a contact and response spreadsheet.

Contact attempts, dates, times, topics of discussion, no call/no shows. Send it out to the family DL regularly so they are less intrigueing to SD for her lies and manipulations.

Document and publish!!!!!

Your DH should clear the air with extended family from SD's poisonous lies.

However if your DH doesnt that gives you a green pass to defend yourself to them. If they say things insinuating you are the reason big daddio doesnt get to see poor damsel in distress SD speak up!  Or better yet if DH is there put him on the spot.

"My that is an interesting narrative. DH can you explain WHY SD doesnt see us much"

My husband's older nephew gives him crap on occasion about us not speaking to SS aka Lying Ingrate and SDIL aka She-Devil, claiming we're holding a grudge over nothing. He also loves trying the guilt trip and dangling the grand spawn like a carrot.  Oh, they don't have a grudge against you, they'd love for you to see their baaaaby.  My husband tried giving the facts but it did no good in our case.  But this is a family of rug sweepers. Take no responsibility for bad behavior, take a short break if it was really bad, then pretend that nothing happened.  One big happy dysfunctional family.  They all know the facts but they want to pretend that we're just holding a grudge over nothing.  

If your in-laws are normal, then he needs to give them the facts.  If they're dysfunctional then no amount of facts will make a difference but at least he can say he tried.  

SD is practicing the "smear campaign'.  Google it.  It's a common technique people with character disorders use to sow discord and chaos.  She knows exactly what she is doing and employs plausible situations to present her case.   
I'm curious as to why DH doesn't invest more effort with his family. Is he tired of their BS and you need to follow his lead? Or is he just lazy and takes the easy way out when emotions and feelings (namely yours) are involved?  

Fake cried on the phone to him claiming he abandoned them to marry me and have kids with me and guilted him for that.

the reality is they cut off contact before i met my husband over lies they knew their mum made together with her affair hubby (they're ok to have an affair and get married, but hubby msrring me 5.5 yes post divorce is not allowed)

that really angered me because skids were refusing to take responsibility for their behaviour and choices and scapegoating us as the problem 

they've never dared to pull this crap on my inlaws because they would put them in their place

In an age appropriate manner.  Pulling the teeth of the toxic, no matter how painful it my be for the Skids to learn, is what is in th e best interests of the kids.  These toxic dipshits don't stop their Carson what a kid reaches  majority.  
 

IMHO

In my case, both MIL and SIL seem bent out of shape that DH ever got divorced. He got divorced over a decade ago and didn't even want to get a divorce (despite the fact that BM has "borderline tendencies" and abusive (as assessed by multiple counselors DH saw over the years, including a couples counselor). Despite this, they are still both angry and BM has figured out how to capitalize on this. She plays the victim and tells them all how terrible both DH and I are. She had one SS tell everyone that DH and I sit around talking about how much we hate her when skids are with us. DH's family are such fools, they believed it...even though it sounds completely illogical. 

Now BM is divorced for a second time (she divorced the guy she met when she was still married to DH) because she met someone else. You figure that might help them to realize that BM is not what she seems, but no. MIL is constantly telling DH he doesn't do enough for SSs or BM. DH and I have a toddler and since DD was born MIL has told everyone that my DH "needs to realize he has three children!"...including SSs who then throw that in his face every time they don't like something he does or everything they are demanding something from him. MIL and SIL have also shown little interest in DD.

Its miserable and it makes me angry and sad that DH's family is so sh$tty. The only justification I can think of is that MIL is obsessed with appearances and her son divorcing made her look bad (in her eyes). I basically avoid MIL. SIL has spoken to me once in seven years. I now avoid her, too.

Zero tolerance is in order.  As they are stupid, teach them how that smells.

Its called "relational agression". She is trying to get everyone to hate you. And choose sides.

SO, since it sounds like you DH doesnt want to take that one on himself (which is what he SHOULD be doing) then its on you. I would document contact attempts, and all that, just using the notes in your phone. When comments are made, you are fully within your rights to mention that SD in fact does nothing to maintain a relationship with her father and every attempt he has made has been met with disregard on her part. Just calm facts without emotion. 

I too have a toxic SD23 - Feral Forger. Since she was 18 and ghosted us, she has moved in and out of Toxic Troll BMs apartment, and this last attempt ended with Husband driving 3 hours north to pick her and her stuff up. He had to clean because she is so filthy and the room she was renting was so trash filled, and before that no contact and since then no contact. I think through the years a few texts asking for money. And last September a request to move back into "her old room" which since she left I have remade into my own little sanctuary/dressing room/fish room/sunset watching room.

She and I had been trying to build a relationship but that went down the tubes when Husband told her that she needs to work things out with me (because he cannot tell her "no, you are not moving back in"). She texted me with "ever since you came into our lives my dad has not been my dad (ie I havent been able to manipulate him and control him and get him to do what I want), you took him from me and blah blah blah child of divorce BS..."

And thats where we are at right now. Im sure that she trash talks me to everyone. Well good for her, shes living her "best life", crashing whereever, no job, no car and no drivers license. Somehow Im sure she will use her "assets" to surround herself with enablers (men) who will be willing to support her. But that will only last so long...looks fade....the masks come off...the truth shines out, like your SD. 

Fact and Truth come out.