How do you convince someone to seek treatment?

I'll try to make this as succinct as possible. Sister has been diagnosed with depression and anxiety a year back. Has moderate insomnia. She is on antidepressants on and off, as well as sleeping pills. She has rejected other types of help, including psychotherapy and counselling, because she deeply mistrusts and hates her therapist.

Recently, she has been developing a few other ailments - persistant for more than 7 months - that are probably related to stress, anxiety, poor sleeping patterns, and poor dietary habits and lifestyles including smoking, going out late at night, the whole shebang. She and the family have tried many different doctors. Initially, she initiated treatment, took her medication, but as her symptoms persisted, she started mistrusting doctors. She is now ambivalent about her treatment, actually stormed out of clinics a few times, and basically didn't take her medication. Her ailments didn't have a quick fix. It probably needed a lifestyle change, which she is unwilling to do. Tried cajoling or telilng her she needs to take charge of her own treatment and lifestyle, to no avail.

I'm only asking this because this is stressing my parents, who have physical problems of their own. They basically took over her care for her - simple things like making her eat her medicine or making doctor appointments for her to bigger things like making treatment decisions for her - which I feel it's unhelpful for everyone.

How should she go about all these mental and physical issues, and how can I convince her to?