Can my family refuse any further medical aid for my Mom (88) who has Alzheimer's and a bad heart?

Yes you can if you believe that it is her wish not to die in a hospital. I'd contact hospice and get them in on this. They will help keep her comfortable and can give you advice. It's hard to do this alone.
Take care,
Carol

Carol's right. Once you sign on with a hospice they take over and it's in the contract you sign with them that there will be no more hospitals and you'll call them instead of 911. Hospice also has a line to the Dr. (their own Dr.) who advises them immediately. No channels to go through. No leaving messages for nurses who then have to leave a message for the Dr. You'll be done with all of that and your mom will have excellent care.

Call hospice as soon as possible.

Care & Comfort offered by Hospice can be IDEAL SOLUTION. Hospital stays often exacerbate confusion and increase anxiety.

As hard as this decision is it is the kindest one to make for someone who is suffering like your mom. As POA you can make decisions regarding her healthcare only if you are listed as healthcare POA. Talk to family and try to make the decision together as to what to do. Do no resuscitate is fine at this point in her disease. They can offer comfort measures at the NH for her and keep her pain free if she declines and no medicine will help her get better. Good luck. I just went through this 3 months ago with my 87 y/o mom. It's so hard.

The question above brings up a point I hadn't thought about.... that I will need to ask my parents if they should became ill, where would they want their final breath to be, at their home, or someplace else.

I know for myself, if I am still alive but going down hill quickly, get me to the hospital or hospice because I don't want my bedroom at home to be always known as "that is where Terry died". But then again, that's just me.

Yes, call in hospice. Without them involved, the nursing facility will be likely to act in the interest of not being sued by a resident's family, so sometimes 911 gets called even when they know the family has indicated that they shouldn't. Hospice helps with that.

I always thought I wanted to die at home, when the time came. But freqflyer has given me something to think about. It never occurred to me that the room where I chose to go would always be that. "The room where she died" Something to consider.