I have read all of Emerald's posts and I don't think she should be the one that has to make nice but that is Emerald's decision to make - not mine, not yours.
I haven't read all of her posts, so you may have more insight into the situation and into her relationship with her sister than I do. I'm only going with this post, and it sounds like she previously had a positive relationship with her sister, one that is important in her life.
What her sister did is wrong, hurtful, and confusing. There is no excuse, and her sister SHOULD make amends. But for whatever reason (pride, defensiveness, selfishness, fear...who knows) she has not been able to do that. Emerald can't make her sister do the right thing, but if she wishes, she can offer forgiveness even when it hasn't been asked for, in the interest of mending the rift. It could open the door for her sister to offer an apology or an explanation. Or it could be met with more hostility.
I also agree that Emerald is the only one who can decide.