YTA, it is not the trend here, but hear me out.
I do believe your daughter is TA for cheating, but your question was specifically if you were TA for telling her now ex-fiance. She now has to deal with the consequences not only of her actions, but of your poor judgment too. You preferred a bf of hers than your own daughter. So now you also have to live as you preach and live with the consequences of your own actions.
It is not your business. It is/was not your relationship, it was her mess to fix. The only thing you were entitled to do since they were at your house, was to ask the other guy to leave and ask her to respect your house and come clean to Bran, give her an ultimatum on this. Yet you make up a poor excuse to deal with this poorly by saying "I didn't want to cause a scene..."
It is your daughter and while I don't approve of ANYONE cheating, there were many other ways of dealing with her cheating. You referred as her sleeping with another guy as "whoring around". I would never talk about my sister as this, let alone refer to my daughter as this. Yet you have no problem doing this... Great parenting! (Obviously sarcasm).
You are more TA for believing that since your wife doesn't agree with you, then she's cheating or must have cheated on you. I don't believe she didn't back you up because of this, but rather she didn't backed you up because how you dealt with the situation and yes, you didn't have your family's back. You sided with an stranger who from now on has nothing to do with your family and alienated yourself from your own family. Your daughter's actions were not right but neither was your poor reaction/handling.
I do suggest you letting things to calm down and afterwards talking with them. It sounds to me from the way you reacted, that you had somehow a traumatic experience with cheating, maybe letting them know... and also reming your daughter the pain she was in when she got cheated at 16... cause now she caused it and remember her of Karma. Anyway, hope it soon solves our for you.