you do not pick her up.  How she gets home is not your problem,. She better learn now, 

This back and forth is why she is dogging you.

Your DH picked her up, like you wanted. She texted DH, like you wanted. She is staying out of your hair and out of your space, like you wanted. And your DH is staying out of the middle of it, which is what you want - to be out of the middle.

You should have thanked your DH for handling it, or just ignored it and smiled. You are getting what you want, but are having a bad attitude with both of them. I mean this sincerely - if you don't figure out what you want and BE HAPPY about it, you're going to be raising your baby alone. Your DH won't put up with this, and he especially won't when you are head-over-heels with your own but continually throw shade at SD.

Make up your mind and STICK. TO. IT.

ETA: What is with the quotes around D? He didn't do anything wrong. If anything, right now you're the one not being a DW. He picked up SD, immediately came inside to greet you, and even showed you affection. Hell, he even ran to thw store so you didn't have to. Why dog on him?

I've been in your situation, sort of.  When I finally moved in with DH, I pushed for him to get 50/50 visitation for summer (it was already specified in the CO that DH could have 50/50 if he wanted when SS was off from school, but didn't really specify how or when that would play out).  I pushed, so DH asked for it and we got it.  I wanted it because I really wanted to bond with SS and thought that this would be a good way to do so.  I also did it because I knew it would make DH happy, and if things went well, when he was a little older we would push for 50/50 year round.  Let me tell you that after the FIRST whole week, I was ready for summer to be over and NEVER offer to help facilitate 50/50 again.  It was beyond exhausting and I was getting frustrated because I was used to having so much alone time with DH and this was just too much all at once.  I was also used to dealing with SS in very small doses and was not prepared to deal with him on a daily basis.  The tantrum that was so exhausting on a Sunday, was more tolerable because I knew in five hours he was going back to BM.  When he was there 50/50, all I could think about when he misbehaved was, "I have five more DAYS of this!" Looking back, there are a lot of things I could have and should have done differently, but I have learned my lesson and have not even discussed having SS around more unless DH brings it up, and even then I make it clear that I will help, but I will not be "mom."

Unfortunately, your 50/50 is not temporary and you are stuck, and it really looks like things are only going to get more and more difficult.  I don't know exactly WHAT was the turning point with SD for you, but it seemed like you two were getting along for a bit before you guys got 50/50.  I understand she is being a bit of a sh!t right now, but I think you can make one last effort.  SD is old enough that you can talk to her about.  I am not advising you grovel or anything like that, but maybe just talk to her and ask whats up.  Tell her that you feel like your relationship has changed and ask if she feels the same and why she thinks that is.  Don't ask her what YOU did or apologize for anything, but maybe tell her that you felt like you guys were getting along and hoped that her being around you guys more would make her happy, but since the visitation has changed you feel like she is in a bad mood and not very happy to be in your home, and ask why that is.  

She may blow you off, in which case at least you can say you tried and get DH off your back about it.

She may tell you she doesn't feel welcome and that she isn't liking this new 50/50, either.

She may appreciate that you tried and try to dial back the attitude (I say dial back because she is still a teenager and I'm sure you are still going to have trouble with her).

Of course you don't have to do any of these things, but I think at this point you really have nothing to lose and she's not going anywhere so you might as well give it a go.

Killjoy doesn't give me those looks anymore.  I keep my door closed.  She's not allowed in our bedroom.  In the rare event I pass through a room she is in, I don't look at her.  Done.

DH can stop her from blatantly disrespecting you, but he cannot make her be "nice" to you.  It seems like you want her to like you.  She may never like you.  It doesn't mean you are a bad person, wife, or mother.  It means she's got a loyalty conflict.  Let it go.

I think some of this is still fresh resentment from your SM "awakening" now that 50/50 has been happening for a while. The other part is probably pregnancy hormones. I swear until sometime in the middle of my second trimester, my DH could not do anything right. I wanted to punch him in the throat just for sleeping (something that alluded me the entire freaking 41 weeks).

Just be aware that little nugget inside you is throwing your moods out of whack and try not to murder them.

I don't think your DH did anything wrong.

I think you're insulted because SD beat you to the punch, and her little comments and tone tell YOU that she's the winner, but DH is clueless about any of it, he's not interpreting the tension.

Enjoy the fact that DH is taking responsibility for her without you having to tell him to. Saves an awkward conversation... and even if the little brat is making out like she won, YOU WON.