This is your husband's problem to fix.  He is the one that needs to do the grunt work with his children.. and he SHOULD make them a priority (like you and your child are also).. They are his minor children and he should be making every effort to be part of their lives as their father.. (not best friend.. not bank account).  YOu can be supportive of this effort but you can't make it happen.

Every time you get accused.. the reply is "your father is his own man and makes his own decisions.. I can't force him to do anything.. he is free to have a relationship with all his children".

When they talk about your child in that way.. it's "when you decide you want to be part of your dad's family.. then you will be able to also forge a relationship with your younger sister.  Right now, when you have unresolved issues and run hot and cold.. that isn't fair to her.. having people in and out of her life"

When they blame you.. they are old enough to also hear that the accusations made a couple of years ago were very hurtful because you have done nothing but try to do all you could for them.. and thought you had a good relationship with them and felt that the accusations were unfounded and a poor way to reward someone who has done so much for them over the years.. "

You have been trained and your brain has been hijacked by the drama and the chemistry involved. I'm sure your therapist could explain it to you.  This is hard stuff to let go of but you must for your own sanity.   Everything they say to you serves a purpose: their's,  not yours.  Everything is not black and white but for now it might have to be.  As you begin to let go, you can decide how much more to do. Nothing is forever, remember that too.  For now you need to untangle yourself from this drama, get your thinking straight, then you can revisit the situation with fresh eyes and see what's what.  you can't predict the future, but you should prepare for it.  Do you want to look back and see how you wasted precious years with your bios, not being the best mom you could have been , because of this drama?    Estrangement sounds horrible but it's what happens when healthy firm boundaries are drawn by one and not respected by the other.  I have found that the one drawing the boundaries uses "disengagement ". The one not respecting those boundaries and making a big stink about it uses the word "estrangement " and it sounds awful.  But is is really??   ( I've been on both sides of this ) 

I think as well as therapy, you might need to trial a medication.

This is consuming and destroying you.

See your GP.

They are correct. You do need to ride DH hard on fixing the issues with his failed family breeding results.

This will not end nor will your mind ever be off of it until you grab a handful of DH's testicular fortitude and continuously rub his nose in the stench of his failed family parenting failures with firm regular reminders to keep his X in her place.

Good luck.

Bluntly OP.. again.. your husband needs to fix this.  and by "fix"  I don't necessarily mean he will reconcile with his kids.. but he has to settle this issue with them.

He needs to communicate with his kids that HE is the one reluctant to engage with them due to past behavior

His WIFE has done nothing but push for him to have a relationship with them when they were younger.. it was only when she became more busy with a child that I, your father, dropped the ball.  It was not at her urging.. it was my failure as your father.

There is also the matter of fact that these girls are technically still children/minors.  They don't get to dictate terms.. and negotiate a settlement in their favor.  If THEY want to be part of his family again.. THEY need to acknowledge the deep hurt their allegations made.. and make some level of explaination and apology for the stress and drama that it caused.

He needs to demand they put in the work with him to repair his relationship.

If he is too "butt hurt" to do that?  He needs to tell them that.. basically he isn't in a place where he wants to forgive anyone.
 

You need to disengage from it all.  When they contact you.. you nicely tell them to call their dad directly... that he has asked that they call him and not you.  and then put it out of your mind.  When people pressure you on the subject of his daughters.. you tell them that you really don't know what is going on because you leave it up to your husband to have his relationship with them.. they are welcome when he wants to have them there (knowing that he won't unless things are good).  Disengage.. it's not your monkey.. not your circus... 

I'm not sure if this will help but this is my perspective. Marrying someone with kids from a previous relationship isn't good for anyone's emotional and mental well being. You are with someone who expects you to put them and their kids first when they put you second or third in their priorities at best. This is not good for anyone's self worth. It is a one sided relationship and it has to feel very lonely. On top of that your life stresses are amplified. People who have kids are more likely to have more severe financial difficulties and close ties to people you wouldn't normally choose to have in your life regularly (exes, in laws, etc.), not to mention their lack of free time and health issues such as sleep deprivation, depression, etc. The question is do you really want this additional stress in your life and for what? Life is hard enough. Their kids will never love you like they love their parents. Society will never acknowledge you like they do the kids parents. Your partner will never get it or acknowledge it. It is not a good place to be. Love yourself.