When somebody's mind 'turns to mush', it means that they cannot think clearly. This could be due to heavy drinking, too much TV, drugs or, in this case, senility in old age, probably from Alzheimer's disease. Saying that someone's mind has turned to mush, temporarily, from drinking is humorous. Using that term to describe senility is considered cruel and tasteless.

Well fdmaxey's answer is perfect. But mush is like, you know when it snows, and then it rains a little bit? When people have walked on the snow, it goes all mushy (or slushy). And when you have peas with your dinner, and you squash them with a fork, they turn to mush. So people are saying instead of having a functional brain you have mush instead. It means you can't think.

Yes you are right, it could mean that she has dementia or Alzheimer's where the brain loses its capacity to function properly.

And yes, saying a person whose mind has turned to mush, when they are in a care home, is tasteless and cruel. My grandma is in one, with mental problems. Although I'm not saying you've done anything wrong, of course you have not. Just warning you about it's proper use.