Sounds to me like your sister might have some guilt and subconciously wants validation for having had affairs. Also it might be backlash, how did you react when you found out that she was having affairs? She might feel that she is able to judge you if she feels that she was judged by you.
I hope that it was just an in the moment reaction to the situation at hand and that she will realize that this is what works for you and you can get back to being sisters and friends.
And like others have said, it's really not ok to take someone's phone to read text messages. Once things have blown over you might want to have a chat with her about privacy, or better yet send some kind or really shocking text message when she's around to really get the point across that sometimes it's better just not to know!