Is chemotherapy okay for those with early signs of dementia and severe depression?

This will be kind of a doozy to read..my apologies.

A bit of background:

My grandmother is 80 years old today. Though she is only 80 it seems she is aging much faster than her other elderly peers. My grandfather died nearly six years ago of a heart attack and my grandmother has lived with me ever since. Ever since his death she has been severely depressed and seems she is only living to die at this point. She is still mourning his death but is also becoming increasingly scared of her own demise. For the past six years I have watched a major cognitive decline in her.

Terrible Year:

This past year she has been unable to catch a single break. In June she received a cortisone shot right before finding out she needed her second hip replacement. She had to wait three months in severe pain for the cortisone to leave her system. She got the replacement in Sept. and is still struggling. She was told she need spinal stenosis surgery but that was delayed when they found a large growth on her breast that she refused to tell anyone about (she has had breast cancer before). They took out three lymph nodes while removing her breast and found aggressive cancer cells in one of them. Now they would like to do chemotherapy to make sure microscopic cells haven't spread through her lymphatic system.

Possible Dementia:

It seems as though no family members will listen to me when I say I believe she has dementia. Her cognitive decline is not "normal aging". I've seen it for a couple years but it has become increasingly severe over the last year. She is incapable of remembering a conversation we had 10 minutes prior. She has become increasingly confused over the last year and it seems like she never has any idea what she is talking about. She tried to tell me I was in my 30s and would not budge when I told her I am only 20. Sometimes it is like she goes back in time and thinks we are in a different year. She has had friends of different ethnicities all her life but is all of a sudden becoming more and more racist, almost as though she is back in her childhood when racism was "normal". It is becoming harder and harder to take her out in public. She is angry all the time and although I know it is mostly frustration with herself she takes it out on those trying to help her. She said to me yesterday for the first time "I always feel confused." This holiday season was also the first time that my cousins started to notice a large shift in her. She asked about my cousin who "ran the Boston marathon last year" which my cousin DID do, but about 14 years ago.

THE QUESTION:

Finally, sorry for making you read all that. Is chemotherapy a good idea? She is terrified of it (and does NOT want to lose her hair) but if it is only for microscopic cells is it worth it? They said the cells could take aprox. 5 years to grow into another aggressive cancer but I am unsure she will still be functioning in five years. I am afraid chemo will do more damage than good for her.