Okay, don't get mad at me please, please - I love you sweetheart.
I want to say that in my opinion, you could have spoken more gently. You could have found a gentler way to speak with a sister than to say she was lying. She bristled a little at the way you said that. And she isn't trying to be intentionally deceitful. She's discussing how she sees and understands. She doesn't appear to me to be one of those who charges into a thread and starts spouting off meanly or arrogantly. Please remember that I love you sweetie!
Remember that I love you if what I said makes you mad at me. I'm giving my opinion.