I'm going to tell my (ex)girlfriend's sister that she had suicidal intentions.
Why would you tell your ex girlfriends sister such a thing?
She called me a cheat and I wouldn't allow this.
It is wrong to betray someone and tell their private thoughts and behaviors to others. You are betraying your ex girlfriend and that is wrong. Nobody is going to trust you in the future.
Her sister needs to know this since my ex probably thinks it's okay to do what she did. She needs to have some serious feeling remorse and regret.
She's your ex now so you have no business in her life. If you think she genuinely has some issues you should help her but you have no right to reveal her personal matters to her family without permission.