Cutting to the chase - you were right to say something, because you had plans that were broken by her and it did appear disrespectful.
You were wrong to swear at her, loose your cool, and say \ act mad even in an email. In her email back, she came back fighting, she was not apologetic.
If it had been me, talking about it quickly over the phone to sort it out ( even with a small cost) would be worth it. You;ve been seeing her 3 years after all ! whether she's lying or not, you did not deal with this great, and it sounds like you've hurt her. When she lets you down, there;s no need to hurt her, just stay in control, be calm and let her know whats what - put her straight about whats acceptable and whats not. easy isnt it?
now your ass is on the line too, when it should have only been hers.
Do you trust her? sounds like your suspicious. A good way to see if she can be trsusted is if she has cheated on any of her previous boyfriends.