If you're concerned about your mum falling again and/or you being unable to give her the care you need then no, you are not being unreasonable.
Several years ago my mum, who lived with my brother, fell on the stairs and broke her collar bone. SS were supposed to be installing some features to create a safer environment and the hospital wanted to discharge mum before those had been put in place.
I refused to have her sent some so she went to a nursing home for recuperation and to give time for SS's to do what was needed.
She was in for 3 weeks; 2 weeks after SS's had been because after just one week there, she wasn't fit enough to go home. There we was no way the hospital should have tried to discharge her, and send her home when they wanted too.