I'm going to break up an engagement
Why do you feel justified in doing so?
Breaking up an engagement is always better than being in a relationship without trust.
I'm sorry that there's no longer any trust in your relationship.  It sounds like the best thing for you to do is break it up, since it doesn't look like it's working out for you.  It will be a good move for both of you in the long run.
I'm glad that you agree.
Of course I do. Staying in a relationship without trust wouldn't last long anyhow.