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I'm sorry to hear about your situation. Traditionally speaking a doctor will look to the "next of kin" to make decisions regarding health care provisions. The eldest child would be the next of kin (assuming no living spouse). Note that this is not a legal distinction, in that the doctor does not have to do this. But there's nothing that says that the doctor has to take into your wishes or direction either (without a power of attorney or guardianship). I assume that she's no longer competent to make a power of attorney to give you this authority. If she is competent and able to understand the nature of her actions, she can still give you the power of attorney to handle these matters. If she's not competent, the only way to force the doctor to even consider or take direction from you, rather than your sister, is to get a guardianship over your mother. And to get a guardianship requires that you go to court, petition the court to be named as guardian, and actually be named guardian. Now it's more likely that the court would grant this to you if you had a closer, more trusting relationship with her than your sister, and if the court feels that the best interests of your mother would be represented by you in this role, it would almost certainly grant it to you. But you would still have to apply.
That being said, you need to contact an attorney in your area that deals with elder law / guardianship cases. Go to www.lawyers.com or www.legalmatch.com to find an attorney in your area. You should be able to find one that will give you a free initial consultation and better advise you of your rights, any problems with your case, likelihood of success, how courts are treating cases such as yours in your area, and what you should do next.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Thank you, ***** ***** luck to you!