Your husband needs to find a counselor that will enable him to see the manipulation and that giving in to it only makes it worse. SD is not the only girl at BM's house. She has managed to live there. Her attitude is pure manipulation.

DH needs to realize that if he continues to acquiesce to SD he is risking his current marriage and his relationship with his children with you. Is he planning to dismantle the baby's room every time SD visits after the birth? Where does he plan to keep the baby when SD deigns to visit?

Your DH needs counseling so he can see clearly. 

I would want none of that drama around if I were pregnant. She doesn't like not being the only girl? Fine. Your DD can be the only girl

She is trying to manipulate him. He should not just give up on her, but he should not chase her, either. He can call her, text her that he is thinking about her, that he loves her, that he would like to see her, etc., but he should not give in to any demands, such as buying her things or doing her bidding. He is the parent, she is the child, she does NOT call the shots.

My SD once also told my DH that he should have tried harder, that he should not have let her go so easy, blah, blah, blah. None of it was easy, she and her mother made it an impossible situation. A person can only do and take so much, even when it comes to their own child.

She is being unreasonable and he should not encourage that behavior.

At age 7 & 17. They one day message my husband claiming bio mum was a changed woman and instructed them to re-establish contact with daddy..

the reality was that their narcissistic pd hcgubm was fuming that since she made the daughters end contact with daddy, several yrs later claiming daddy abandoned them to marry me, the reality was bio mum was so used to my husband jumping through hoops for them except now he had a wife and 2 young kids with me and we are all pleasant to be around, unlike skids.

they sure as hell guilted him for marrying me and having 2 new kids, calling us his new family repeatedly. Hubby reminded them that we were just as much hubbys famiky as they were and they expected he be feigning, fawning over them and dropping everything and jumping through hoops for them. Imagine the shock when that didn’t happen??

what is the result now? They do no contact for months until they need favours or to maintain daddys monthly allowance 

Just how much power over his life is he willing to give over to SD ?  If she wins this round , who is next in the chopping block? Her brothers? After that will she insist on a divorce for him?  
 

He's running scared now , unfortunately he has lost his mind.  This has BM written all over it.  I had a SD very much like like this and gave my DH the ultimatum that if he didn't get rid of me he wouldn't walk her down the aisle. She was 15 at the time and no sight of a fiancee in sight.  ( definitely from BM) Needless to say he chose me and SD went her way. It took him therapy with a wise old man who had been thru it with his own daughter to put it all together in his head/heart.  Taught by their mothers, they only saw dad as someone to fleece and use.  No love involved.  My BM has the same experience being alienated from her dad by her mother. She knows no different.  
The bosses lesson my DH learned in therapy that took time to assimilate into his heart and thinking was to love the ones your with.  He can still love SD but from afar so her toxicity doesn't ruin your lives.  
 

OP, you are going to have to put some rules/boundaries in place to keep your home under your control and not SD/BM's control.  Make sure his chasing isn't putting the family in financial troubles. Keep her away until she can behave like a member of the family. DH can see her outside and give him a budget for these expenses.  Maybe cash only and take his cards if he can't discipline himself.   
BM will throw a fit but put her in ignore. There is no pleasing this type and she is not unique. Many of us around here have been thru this exact scenario.  It's best to drop the rope and give them what they are asking for.  
Tell your DH for me that he is a person worth more than what his daughter is giving him. He and you deserve to be treated like human beings, not to be used for materials things. 

She is 14.  She does what she is told.  Your DH is his own biggest problem.  He needs to quit tolerating her crap and catering to her manipulative toxic juvenile manipulation.

I am not in favor of hitting children, but in this case, this little brat NEEDS a good old-fashioned spanking, in FACT it is WAYYYY  overdue. I cannot believe your DH has allowed her behavior to come this far!!!! I understand some parents will do sh*t out of guilt, but to allow this from a 14 year old??? Ridiculous. She will be doing you all a favor by leaving you the hell alone. My inner Latina-mom side wants to come out and smack this girl with a chancla through the screen, just by reading this!!

This is textbook parental alienation. I don't know how he can "make her" come over, but yes, he should show up to get her as planned and see what happens.

There are those who will tell you to go to court and spend your retirement savings fighting her refusal to visit, but those of us with experience in alienation know this doesn't work. The court knows too that you can't really make teenagers do anything and it's easy for BM to make herself look like she's encouraging SD to go and she won't go. So court, most likely, would be a huge stress and a waste of time and money.  Also, there will be people who say to beat her and make her behave, but unless you want to enjoy a CPS visit during your pregnancy, I wouldn't do that either.

When my SS stopped coming over, DH stayed in touch, texting him here and there, letting him know the door was open and he could come back in our lives anytime. He didn't beg, or grovel or try to force him or buy him.  And here's the key - we learned to survive and even thrive. Our lives got better without the constant stress of SS being alienated and the endless fighting with BM.  DH was able to let it go and move on. SS returned to our lives 3.5 years after he was alienated.

I do agree that a therapist with experience in parental alienation (for DH), might be helpful. Fighting and trying to force her, or going to court, will likely increase the alienation. Groveling sets up a dynamic where she will use your DH financially forever.

This stuff is all very hard. 

If you and DH were a childless couple and all you had to deal with was SD14's behaviour then you'd actually have a real decision on whether or not to stay involved. But you've got young bios who need to be protected from this toxicity. This behaviour is exactly the sort of thing my DH's daughter did. And with BM egging her on in the backgroud it doesn't stop when they reach adulthood. Not the dynamic you'd want your boys and girl to see and think is ok. 

I agree with tog that this sounds like classic alienation. BM is probably telling her that now that your DH will have another girl who won't love her any more and he doesn't put in enough time or spend enough money on her. 

I also agree with the counselor idea. Your DH could go on his own, but he might also consider going to a session or two with his child. 

One child is partially alienated from DH. He stopped wanting to come to our home, didn't want to do things with DH that he previously enjoyed, and was regularly upset about things that should have been non-issues. In her zeal to make DH look like a terrible father, BM demanded that he go to counseling with this child. I think her assumption was that the counselor would tell DH that he was a terrible person and SSs time should be reduced. Instead DH cried and told SS that he loved him and didn't want to lose him, so he wouldn't fight to force him to come to our home. SS cried and told DH "I talk to my mom about my relationship with you all the time and she says it's bad." The counselor pointed out to him that it didn't seem like he had a bad relationship with DH and he was lucky to have a father who clearly loved him. BM stopped counseling shortly after that, but as soon as DH made it clear that he wouldn't force SS to come to our home, BM then started forcing SS to come to our home. All that is to say that there is a large chance that this is actually coming from BM and not the child. 

I think pandering to your SD is not the answer. Your DH may have to let her go and hope she comes back, but trying to jump through the hoops that she (and more likely BM) is setting for him will be a losing battle. This is about power and control and she has the upper hand because she knows that he wants to see her.