So - this is a young woman who longed for her mother to be in her life. You replaced that to some degree, but not really - you weren't her bio mom. Now bio mom is back and she's toxic. She's making clear to your SD that she must be loyal to HER, BM, or risk losing her again. 

Personally, I'd just take a step back and let DH rebuild his relationship with her. She will eventually see exactly who bio mom is and then she will be willing to have a relationship with you again.  Don't chase her or let her use you. As you said, having your mother abandon you is extremely traumatic and your SD has to work through that. Don't take it personally.  My guess is that within the next couple of years, BM will do her wrong in a really big way and she will see the truth.

She needs time to experience her mother, warts and all.  As for you, its a waiting game.  Love the family that does come around, don't let SD sow any seeds of separation between you and DH.  Keep the marriage strong and first priority.  This relationship with her father should be rebuilt with him first.  She has a lot of hurt to make up for but she has to understand her mother before she can let him back in.  Living with BM daily for so long gave her ample opportunity to " brainwash" SD into believing her side of the story.  

Don't  let DH let lies go unchallenged, encourage him to get SD to remember the good times when they meet.  SD will struggle coming to terms with all of this and he will have a tough time of it.  Hopefully the two of them can work it out and rebuild  a connection.  

My DH is estranged from 3 of his bios.  None of them have reached out to make amends yet.  He's doubtful they ever will. If they do, it on him and them to figure it out.  I'm just DH's cheerleader and wife now. A much better role than evil stepmonster. 

I agree with tog redux.  The BM in your SD's life is emotionally toxic and chaotic - and the chaos is being reflected in your SD's communications (or non communications) with both her father and you.  I would advise both of you to be cautious in your dealings with her and hold her at arm's length.  I think it was very inadvisable for you and DH to invite SD on holiday w ith you, just confine any communications to brief friendly messages, at the most she and DH meeting for coffee and a chat.  Anything else is asking for trouble in the present circumstances. 

I agree with above posters. I also feel sad at the sheer amount of hard work and love you both put in to be treated like that (someone may have told her stuff that is not true, or something like that).

If she doesn’t want to be told what to do (as many youngsters like to state when they think are a mature, but not....

you might wish to phrase sentences to her in ‘gentle way’ such as 

“you might like to try this, or one possible solution is such and such”..

if you have tried that already then I’m out of ideas. 

I just know I only see my bio mum a few times a year as I find her intolerable for many many reasons. 

One of them being her saying 

“you CAN’T do that” in a very very stern tone of voice

BM is panicking.  If SD pursues education and a viable career BM's free ride of milking SD and her family will likely come to an end.

Her contact with  your DH is clear evidence of that DH needs to tune BM up with reality and the clear foundation that DH will never abandon his daughter to be BM's beck and call girl since it is long past time for BM to grow up and support herself.

Lather, rinse, repeat.

I’ve seen this or such happen so much, there is little anyone can say about how to remedy it.  “ After the phone conversation, my husband started getting texts from BM (though they had not had any communication in YEARS, we assume his daughter gave her his #) she told him that he was a horrible Father, that he needed to leave their daughter alone and keep his toxic wife away from their daughter.”

Yes, it is true!  BM can literally be a drug-addicted ho, and no matter what, the children will always want their mommy and welcome her back, anytime, with open arms.  This will occur even over the bio-dad, much less a SM, even though they may have been there for them through thick and thin for years and years.  All I can say is, what it is, it is so deep, no one will ever break the code.  It is something in the DNA, quite literally, is all I can think.

SO, given that, there is very little a non-BM can do.  Very little.  You’d think when it came to adulthood, common sense would prevail, but it doesn’t have much to do with common-sense; it has to do with biology, and million and million of years of it, all that was spent on creating the mother-child bond so the future of the species was as secured as it could be.

So, when you ask for suggestions, it is no where near as simple as one might think or as some so often like to say—"Oh!  Give it time.  She’ll figure it out.”  Maybe.  Maybe not.  Whatever happens it will be between her BM and her.  It will have little to do with bio-dad or you, even though you two basically raised her. 

And, yes, this is another example where SMs suck it up and take it for years and then get screwed.  Putting the biological 50:50 aside and given the psychological, pretty much unbreakable mother-child bond, I’d say in real terms, your SD currently belongs to her BM 85% and bio-dad 15%.  As hard as this may be for you to hear, you need to stand aside, let your DH handle it, and concentrate on your own children.  She is lost to you now, and some people will try to argue that she never belonged to you, that she always belonged to her mother.  Yep, in some ways she did, but as SMs we are never told that.  We are just told to suck it up and take it and wait for our big pay day, which too often winds up being a big kick in the caboose.

One big caveat, though--your DH should always be treating you like the wife you are.  You are also a mother to your own children.  DH and his adult daughter should not be going on daddy-daughter dates.  Grade schools kids might do this once a year or so, but adults respect the husband-wife relationship.  They don't get a pass on this just because of a divorce or seperation years ago.  Your husband should tell her:  "You and I, as father and daughter, are a package deal, but my wife and I, as husband and wife, are a package deal too.  You are my child, but you are an adult; adults are to fly away and find their own life-path at some point.  Spouses, on the other hand, are to be bonded for life, 24/7.  It is not a tit-for-tat situation where you can get away with trying to force me to decide who I love more.  So, if you choose not to accept my life partner, my wife, then you've already made my choice for me.". 

I have a life long childhood friend who long ago wrote off his mother.  He was raised by his dad after his parents divorced.  His sistrer was rasied by their mother until she was about 10yo at which point my friend took his sister, ran away from mommy's commune and called his grandfather (Mommy's father) to come get them.  They called their dad when he got off the plane returning home from dropping him off for visitation with his mother.  His dad immediately jumped on a plane and flew back to get both of his kids.  His former FIL backed him in court to get custody of his daughter and to stop all visitation except with GrandPa who would not tolerate his own daughter to remove his grandkids from his home if she came to see the kids.

Even his sister has written off their mother. Completely.  The last time either of them saw their mother was when she came for his wedding.  He and his fiance invited her to their house (small modest home in the midwest) to have dinner with them and his sister.  Mommy showed up and stayed for 15 minutes went out on the front porch for a cigarette, got in her car and drove away never to be seen again.  His Grandfather showed up that evening , he flew in from out of state for the wedding, and asked where his daughter was.  Jeff told grandpa what happenned and even her own father wrote her off at that point.

Toxic really does have no place in anyones; life and should not be tolerated even when it is a parent or even a child (adult) who is toxic.

Begging for a toxic mommy (or daddy) to love you and beging them to stay in your life is not the way to deal with toxic.

IMHO of course.