"Was I supposed to interfere and say something? "

Not in the middle of Dad's useless little lecture. No. The time to discuss your differences in parenting tactic and come to agreements as to how the two of you will stand together in appropriate rules/expectations and consequences if prior to him calling the daughter in. I agree that Dad is too lax in his monitoring his kids internet/phone usage and that teens running wild on the items deserve to have the instrument removed.

Your ideas as to what should happen are correct, just of the timing of it. For one, kiddo will run all over both of you if she thinks she can pit one adult against the other. Especially if SD picks up on the fact the Daddy might defend her against mean ol' SM.

Considering that you are pregnant with his children, I would be concerned about what kind of a parent he's going to be to them.

My DH would have done a lot more than say, "Don't do that," had his daughter ever done something like that at that age. But, if he hadn't, I don't know what I could have done about it.

I guess it depends on what kind of relationship you have with your SD. Do you feel comfortable talking to her about it? I would at least try to stress to her the consequences of putting things like that on social media.

It could be he just didn't want to deal with it at the time and was half asleep.

Congrats on the twins! That must be exciting and scary knowing it'll be double trouble!
Teenagers and inappropriate internet usage is a common topic these days and its another on the long list of behaviours that are that much harder to tackle if the two households are dealing with it (or ignoring it) differently.
Clearly you need to be having a sit down with your fiance and seeing how big a deal he thinks it is, personally if hes already "spoken" to her hes already dealt with this instance so it'd be wrong and too late to now give additional punishment for it but clearly you are going to want to be telling him that either you or he needs to be checking her online activities more frequently. Explain the dangers and all the lectures to SD and on the next occassion she looses internet access, etc. Its going to be a toughie but hey what in life is easy?

Dont worry about HRNYC, you are never going to be doing the right thing. Now you are in the bad books because you are living together, unmarried and pregnant! Such a scandal that it is, but had you gotten married before living together then you'd be being called foolish for rushing into marriage.
I dont buy the whole bad example thing, because lets face it, how many of us waited until we were married before having sex? Teaching good morals about sexual relationships isnt about pieces of paper to state you are married or not, its about teaching the individual to have respect for their bodies and other people. One of the reasons theres so much "under age" sexual activities (in my opinion) is because the media and porn industries make sex out to be something its not, young hormone fuelled teens get a completely warped view because their parents go on about sex within marriage, if they broach the subject at all.

So back to the point of the Original Post which has nothing to do with OPs marriage status…

Your Sd is one of many girls that are doing this. Some parents don't think monitoring their youth is a big deal. Even though I agree with you about it not being acceptable social media content, I really think you brought this on yourself. You went snooping checking for trouble, you found it and woke up your DH to deal with it. He dealt with it in the way that he saw fit. You can tell him that you don't agree with the way he dealt with the situation and that if you y'all have a girl or two that they will be held to a different standard of self respect than he has for his own daughter. But that's about all you can really do in a situation like this. Teens will be teens hormones and all. Twerking is atrocious in my opinion but its also not as bad as it could be in the big scheme of things. I will tell you this that as mad and disappointed as you felt seeing her acting like that is nothing compared to how disappointed your SO probably felt seeing his baby girl acting like that for all to see.

Good luck trying to raise viable adults with this idiot as the father. On any number of occassions during our brain fart teen boy years when my younger brother or me shoved our heads up our own asses mom and dad owned our idiot asses.

Your donor can't manage to raise a single child to a state of reasonable judgement and behavior, how do you or he expect to be successful raising twins together?

IMHO of course.