sometimes I wish i had never had kids. I didn't mean it for one moment but just that divorce would be much easier without them
Ah, well this is very different from "I wish you'd never been born". Easier to recover from what you said.
Firstly, do you think your DD knows that you love her, and really don't regret you had her? If you're confident of this, then you can proceed with a "sorry I lost my temper and said awful things, you don't need me to tell you that you and your brother are the best things that have ever happened to me. I just hate doing all this divorce stuff, it's fucking AWFUL".
If your DD is feeling especially fragile after her father's appalling rejection at Christmas, then I think you should go in much heavier. She's 16, she will have an inkling of adult emotions and stresses. The truth is, your comment was actually about the divorce, not about her or her brother. You said the divorce would be be easier if there were no children to contend with (true), not that your life would be easier. You could, depending on your DD's personality, explain that you were talking to her at the time as though she were your peer or a friend, rather than a daughter who needs her mother and at least one present parent - and that you regret doing this, it wasn't fair to her.
You should also make it clear to her that the stresses you're going through are 100% down to her father's unfaithfulness, what it's done to you as a person (not a wife or mother - a person), and how angry and resentful you feel towards it. How you hate what he's doing to her, and how angry and bitter that makes you feel. None of these are excuses, they're explanations and you will work hard to make sure that she doesn't hear any more explanations from you, that you acknowledge she needs a parent in you and not a friend.
I think you could turn this around, potentially. You and your daughter have both been roundly rejected and dumped by your ex. There's community in that, but you have to be the grown-up. She's just a kid who desperately needs a mother and a parent in her life.
I'm so sorry your ex is such a dick. Men can be fucking awful sometimes.