If I may... it sounds like you did do a teeny thing wrong, in asking C out before you'd gotten your primary partner's full go-ahead. From what you've written, it sounds like S has never gotten comfortable with the idea of your seeing someone else, and from her perspective it might look as though you used her being out of town to go behind her back and do something she wasn't okay with.
Before I sound like I'm on the attack here, let me say that I'm almost 100% on your side. An open relationship of any kind should be at least theoretically open both ways, unless both partners are truly comfortable and happy with a different understanding.
BUT that's not to say that "being in a V" is all you need before having a fully-developed, open-on-all-sides poly arrangement. It sounds as if you jumped straight into the mindset of, "we're poly now, so I can have other partners" without working through S's feelings about that first. That's the wrong way around. For success in polyamory (or in whatever) you need to start by figuring out what each person's needs and comfort levels are, dig deep to solve any serious conflicts in those, and then express your labels and boundaries.
Also, just as a matter of courtesy, I would ALWAYS expect my bf to tell me he was planning to ask someone else out before he asked her. That's part of being primary, to me (I'd be curious to see if anyone else here, as a primary, feels differently.) That way we could talk through any hesitancies or insecurities I had... or, more likely, I could give him a pep talk and/or advice on how to best approach her. (Or, you know, some of both.)
So, I wouldn't say you made a mistake in getting involved with her or pursuing a relationship, but I do think you could have approached it better, in a way that made S feel more reassured that she would still come first with you.
Now, going forward: I think you need to separate your (justified) resentments and feelings of unfairness from your desires for the shape of your life. Yes, it's totally unfair: you adjusted to her taking a lover, you overcame your initial discomfort and developed a close, stable family with your wife and D; she failed to do the same thing for you. But, like they tell us when we're kids, life isn't fair. Since I've grown up, I've amended that to, "Life isn't fair, but it can be happy." The sooner you can let go of what would be fair and focus your attention on what would help you be happy, the better this process will go.
Ideally, your wife will realize (with as much communication from you as is needed to get the point across) that she owes it to you to overcome whatever issues are keeping her from feeling able to share you. Neither of you should expect an overnight change, but it should be something she can work toward. If she can't or won't do that, then you have to figure out what would make you happy (or least unhappy): a) being with her and D in the current, unfair arrangement; b) being with her but cutting D out of your lives; or c) walking away from them both. Only you can answer that. Hopefully she will see what an awful choice that would be for you, and work on her own growth so as to make it unnecessary.