Expanding a bit on what Joel said as his first point, it would be pretty useful to figure out what, if anything do you want your sister to do to help repair the rift. If nothing else it at least gives you a convenient response to most of the above statements

    - I wish we could have a happy family dinner
    - Get her to do <THING> and maybe we could have it

    - She reached out with texts
    - When she reaches out with action by doing <THING> the healing can begin

    - This is the way things are, you need to accept it
    - I'll accept it after she does <THING> until then the way things are is that I don't talk to her and YOU need to accept THAT


And so on. But Ideally it would be something meaningful that if done would genuinely reassure you that she won't do similar infractions in the future, at the very least