My sister has two children, 19 and 21. She loves them of course but she does not trust their judgment. She discussed with me the possibility of her giving me a healthcare power-of-attorney so I can make decisions on her behalf, especially when she is incapacitated. My question: how strong will this POA be if her children decide to challenge it ? What can she do to make the POA as strong as can be so that it will withstand any challenges from her children and ex-husband ? Thank you.

She will need to have the POA drawn up by an attorney.

A POA, a very simple document, is as strong as it needs to be. Your bank will have a form (ours was a checklist of different kinds of POAs).
But health decisions usually get very complicated, so check your state.gov for an advance directive form (probably about 3 pages instead of one line).
Have notarized copies made for your sister and your doctor(s).
Keep in mind that as you and your sister age, you may want to make changes. She may not be able to accept the responsibility as long as you live.
And your doctor is even more important - you need to be sure he or she realizes what you want and agrees. Some don't. And some hospitals ignore them. It's an ongoing process.

I don't see that her children would have much of a case, but to be sure she should have it done by an attorney, who should be sure to discuss with her all of the ramifications.

In addition, she might consider a few other things to make it "extra-strong":

Record on video the discussion with the attorney.
Have a session with a mental health professional at the time she executes the POA, and get his or her professional opinion that your sister is mentally competent.
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This is also known as a health care PROXY. It is filed with the physician and hospital and allows a designated third party to make medical decisions when the patient is incapable.

Thank you ! You guys rock. I appreciate the advice.

An Advanced Directive, or a Living Will. Is a legal document that allows you, or your sister, to outline the decisions about your medical care, or end-of-life care should you become mentally incapacitated.

The Durable Power of Attorney names your proxy who is the person that is able to make decisions for you should you become unable to make decisions.

In the hospital setting, it is best if you have both a Durable Power of Attorney as well as an Advanced Directive/Living Will. This is so that the person holding the POA can make decisions for you should a particular situation arise that is not covered in the Advanced Directive/Living Will.