Veeg.
Again im going to suggest that depression is not what is at heart of these issues but rather emotional vulnerabillity and emotional dysregulation.
Having a sister with serious health issues tend to deprive a child of needed energy and attention. Having "unballanced" (to say the least) parrents does not make the situation better. Growing up in a harzardous and poisonous enviroment will often leave you with the emotional equivalent of a 3. degree burn-wound: Someone who will experience all touching as painfull and who will apply desperate meashures to manage their pain.
Often there is failure on the part of the family to teach their child to manage emotions by anything but the crudest methods and most succumb to methods of regulation that are very effective but selfdestructive to the extreme. Self cutting and other para-suicical behaviors are common amung theese victims. So is alcohol or drugabuse.
What can you do?
You can do a lot but it will probably be an extremely frustrating process and one whrere you will have to learn from failures rather than from succes.
Having at least one safe relationship will mean a lot to her and will be a stabilising factor for her.
Do you want to do more? How exactly do your se your role in this relationshop? How many resources can you apply to this?
Exercise is fine but just one of a host of strategies that can be applied. There is a very accessable book on skillstraining by Scott E. Spradlin, "Dont let your emotions run your Life" which is based on the principles and methods of "Dialectical Behaviour Therapy".
Some of the discussion in this thread might apply
http://www.uncommonforum.com/viewtopic.php?t=1406