This is heart-breaking for everyone who loves your sister, I’m sure. Sadly, the answer to your question is that you can’t help someone who refuses good help. Her refusal is part of the illness which makes a circular dilemma: Her failure to engage in treatment contributes to the maintenance of the illness. Her illness makes it unlikely she will engage in treatment. This is what severe and persistent mental illness looks like. The ray of light in this situation is that your sister is safe and cared for in the facility. It’s unlikely a suicide attempt there will be successful.
My best advice to you at this point is to let her counselors and other people who support her do their jobs. It is far more useful for you to focus on the people in the family who need your love and support. Visits with a family therapist may help everyone come to some peace with your sister’s decisions and may alleviate any guilt they are experiencing about not being able to influence her to get active in her treatment. It’s normal to experience this as a kind of grieving. A therapist may give you and others in the family some guidance about how best to help your elderly mother deal with her feelings about her daughter’s illness.
If there is a chapter of NAMI (National Alliance on Mental Illness) in your area, I urge you to attend some meetings to see what they have to offer. Often they provide support groups and informational meetings for family members that are very helpful. Here’s the website. The website has useful information about mental illness and the effects on both the individual and their family members on it. There is also an online discussion group. As is the case with any grassroots organization, the quality of local programs depends on who is leading the group at the time and how involved the members are willing to be. But do give it a chance.
There are also forums here at PsychCentral that may be helpful. People from all over the world who have similar issues provide each other with information and support. Click on the “Find Help” tab on the home page.
I wish you well.