Just let it go. Stay in touch (DH should) in a warm and friendly way, but no begging or scolding or I miss you, yada yada.  "Hi SD, how's things? Wondered how school is going, give me a call, love you, Dad" or something like that. Don't chase her and apologize, that gives her too much power.  She's still speaking to you, she's just making a choice she was offered. 

Unless you want to kiss her As*. And tell her she can treat you like a turd.  There is nothing you can do.  This is SD trying to control your home.  She thinks that you will give in. Buying her a new iPhone, tablet, gaming system to get her back.   
Then again BM did not take her on her vacation,  would your DH do that. Or insist SD come along 

Its coming up to Christmas time. I foresee SD getting to be more friendly to you.  Early enough so you have time to buy her gifts. Do not spend any of your money on SD.  She will start the same sh*t on Decdmber 26 

My DD18 did the same 2.5 years ago and never came back......same story you just told...like exactly....even down the "I've been busy with school" texts as the excuse for not replying to texts. Even down to her not giving a shit about DD2.5 who adores her......

i let it go after about a year.....and that's that. She comes around being nice on holidays and her birthday....then it's back to being a huge jerk to everyone in my house the moment it's over......

unless we kiss her A$$ she is rude and mean...

I am done.....

I re-read your other blogs.

Shes doing what SHE wants, and you guys are all chasing her.

SHE made her decision. Personally I would not have allowed her make that decision, but it is what it is. Thats why there are visitation schedules so that both parents can hopefully bond with their child before they leave and launch at 25...jk.

SO, I would stop reaching out. She didnt really like you or your kiddos BEFORE, she has stated that shes happy there, your other blogs state her behavior is the same at BM's, so I would leave it. Do not even start "encouraging" your DH to pick her up. Its his call. Everytime I have tried doing that it bites me in the butt, so save yourself more heartache.

Put that energy into your bios.

SD15 is making what she considers a very mature adult decision, so respect it. No gifts, no cards, no "hey wanna get a bite to eat?" Treat her as you would an adult family member who told you they don't want to talk to you anymore. I know it's hard and it breaks your heart, but sometimes you have to let a$$holes go be a$$holes and not let them control your life and emotions.

I agree with the PPs who advise you to let go, and not chase.

This is one of those things in life over which we have no control. It's like a little death (not the French kind), with a lot of the same feelings of grief and loss. And it requires the same coping skills to get you to that place of acceptance.

If you chase a dog, they'll just keep running. But if you walk away, they'll follow. It's up to your DH handle his daughter, and hopefully he'll keep a line of communication open but not pander or beg for crumbs. Just try to focus on making your home life and marriage as loving, peaceful and positive as possible.

It's not your fault. These things are not so simple, in most cases. There are many variables that factor into the family dynamics. Don't take all that weight on your shoulders. 

As for SD, like others have said, I would not chase her anymore. Doesn't mean I wouldn't send her a text every month or so to say hi or exchange a pic, but I wouldn't ramp up any efforts beyond that. 

I relate to your story, OP,  it has been over a year now since my SD now 17 has lived with us. I met her when she was 7, and things were great in the beginning.  I saw that she was catered to, but naively didn't think about how that would impact once her dad and I were married.   He had 50/50 custody of her and her brother, and she was definitely favored, only because she is definitely the more vocal and demanding of the two.  I think as a single dad, DH found it easier to go along with what she wanted, not to mention feeling divorce guilt.  The problem was magnified bc BM catered to her also.   She was a sweet little girl so it was easier to overlook, until she was around12 and the attitude started.  She could be disrespectful and downright mean to her dad and he would still hop to do what she wanted. I couldn't stand it, and I didn't like the feeling that basically she ran our house when she was here.  When I would try to talk to him about it, he would get defensive and we would fight.  I started shutting down, went through a depression, and withdrew a lot.  I also requested that she give a heads up before coming over when she was at her moms, she had been making a habit of popping in at random times almost every day, and I didn't feel like I had privacy.  I know she took that as I did not want her here, and i feel guilt about that. I wish I had handled things better. 

It got to the point where I was ready to leave, but DH and I went to counseling and that helped our relationship a lot.  He was able to admit that he did often parent out of guilt, and that it really wasn't helping anyone (and I was able to take a softer view toward what he is going through).  He started to make some changes of being more firm and consistent, which she did not like. There was a lot of drama over a couple years, where she would not come over when she was supposed to because she was mad about somthing, and called him a lot of awful things.  But there was still a halfhearted schedule, and a few months before she stopped coming over, I did have a talk with her and told her that I was sorry if I have ever made her feel unwelcome, but that I do love her and really wanted to work on having a good relationship. Things got better for a few months after that.

By this time, she was 15, and one weekend she came home from a party falling down drunk.  There was drama after that, ultimately BM was not willing to enforce any consequences, and when DH tried to, BM "rescued" SD from our house and SD decided she did not want to live here anymore.  And has not since.  BM gave SD the master bedroom, her new leased car once she got her license, and lots of freedom, and what kid would not choose that.   It has been a rocky year, with periods of time where SD will not communicate, times where she is hateful, and times where she is ok.  Currently we seem to be in an ok time, she is communicating a lot with DH and has been coming around. 

I don't trust that it is genuine just yet, but I pretend that I do.  DH chased her in the beginning, and that is when she acted the worst toward him.  He finally stopped, although he would still send a text every now and then to let her know he loves her. I don't know if that is what helped, giving her space to realize she needs her dad.   I do not reach out to her, but if she comes around I am friendly and interested.  I encourage him to invite her to dinner from time to time.   I think someone else said they are kind of like cats, and I thought that was accurate.  If you give them room, eventually they come around. 

I don't know if any of this helps, but I read your post and it had me thinking about my situation.  The hardest part is the guilt, and feeling like since I am an adult, I should know how to deal with all this.  But there is so much that factors in, it's truly a complicated situation, and it's not any one person's fault. I have found that being patient and letting DH take the lead has worked best, ultimately she is his daughter and it is most important to me for them to have a good relationship. Right now I am just trying to play a supportive role.  It makes me sad to think that she and I may never be close, but I have seen enough improvement between us lately to make me hopeful that some day we can at least be good with each other.  It sounds like you and your SD have had a foundation to build from, and hopefully she will remember that once she has a little time to miss it.   These teen years are definitely no joke, hang in there!