Well, I don't know the history of your daughter, but I do know one thing. Who our grown children choose to marry, whether they like us or not, is up to our grown children and if it were me (and it HAS been me) I would grin it and bear it. It is not a mother's place to start conflict with a grown child's spouse. If the spouse is especially abusive and your grown child will not intercede, to me then it's time for me to back out and see daughter alone or, if necessary, have minimal contact, but I don't think it's fair to cause trouble. We married who we married. They are allowed to marry jerks if they like and it isn't our place to stir the pot.
If your daughter cheated, and I have no knowledge of the history behind it, to me, in my mind, she did something morally wrong. However, again, I would say it was not a good idea for you to get in the middle of it. It's not so much, in my opinion, that you betrayed her. You got involved in something that is none of your business. Their relationship between each other is nobody's business but theirs. How your daughter deals with her infidelity is her decision, not yours. Don't blame your daughter's behavior on your own. Your daughter is responsible for what she does and you are responsible for what you do. It isn't your fault that she cheated, but in my way of seeing things it is your fault for telling her husband about it.
I would definitely apologize for getting involved in something that was not your business, then take a back seat and see what happens. Go on with your own life. Usually we do better when our adult children grow up if we accept that our relationship is not going to be as close as it once was, especially once they are married with children. Adult children do not normally hang around with their parents. We didn't and they don't. Some are closer than others. It is not good to become enmeshed to the point where you feel you need to step in and cause trouble because spouse is not in your corner. Also, just because somebody is nasty to you, that doesn't mean you have to reciprocate and continue the nastiness. What's the point?
I would concentrate on your own life and let your daughter live hers. You will regain more of a relationship again if you don't cling to her and MOST CERTAINLY do not tell ANYTHING she confides in you to anyone else, unless it is that she is going to kill somebody else. There is no reason than safety to tell anybody what your daughter does or says.
I do not get involved in my grown children's relationships. It has made us all happy and the "kids" (who are no longer kids) feel safe if they confide in me because I keep my mouth shut. I have to say, none of my kids have ever cheated, but, if it happened and the adult child told me, I would keep both my negative opinion about it and what she told me to myself.
I hope you can find a way to work this out and am really very sorry you are unhappy right now.