It is a sad story indeed. It was a mental institution firstly Erdington House, then Highcroft Hall, then hospital, over the years. It was not used as a normal medical hospita (but it may have been during the war, I don't know for surel.
I would not get worried about it if I was you, in days gone by people used to be put away for all sorts of reasons. Epilepsy, for one. Depression for another. In my particular case, this was my grandfather's sister. She became pregnant apparently by her brother (but which one we don't know), and was put in the home by her father, who I understand was a bit of a brute. I am in touch with a member of the family who used to have her visit them. She was picked up in the car, taken for a day to join the family (her neice's home) but she spoke little, and when she was driven back, she just used to get out of the car and run into the building without looking back. She was not mentally unstable initially, but I think it must have 'rubbed off' on her. The nurses in there used to treat her very well, she used to help with the other patients, and apparently used to do the most beautiful embroidery. She was happy in a limited kind of way. I don't know what happened to her child, but I believe it was a boy.
I suspect your great nan would have been in the asylum, but don't go thinking too much into it, it may have not been much at all. What was the cause of death?