My mother died from dementia. After she died I specialized in the care of Alzheimers and dementia patients.
The brain that is suffering from dementia resembles fine swiss cheese...really. It can weigh as little as half of a normal human brain. The last part of the brain to remain functional is the part that remembers and enjoys music, so if you love your great-grandmother, buy her an Ipod and load it with all the most popular music from when she was about 15 years old. She will really love to listen to it.
As her memory deteriorates, she will still be able to remember perfectly any incident from her childhood and youth, and she will still be able to talk about that.
People with dementia can be emotional, but can sometimes only operate on strong emotions like anger, and they may try to provoke others to anger. Activity such as you mention is also normal in dementia. Try not to make your great-grandmother feel that she is behaving abnormally. A tiny part of her knows that, but she can't control it.