Is it permissible for my mother to give charity every day in Ramadan on behalf of my disabled sister, who is 14 years old and unable to move or speak except by gesturing?

If your sister is of sound mind, an adult, and is permanently unable to fast according to doctors' reports, then she must pay the fidyah (expiatory payment). If she is unable to pay it, it remains a debt upon her. Her mother is permitted to pay the fidyah on her behalf with her permission. However, if doctors determine that she will be able to fast later, then she must make up the days she missed.