How do I deal with my mom who is 77-years-old and has had a stoke leaving her unable to use her left hand or left leg?

Is your mom receiving, or will she soon receive, in-home physical therapy? Stroke recovery is greatly enhanced by this. Your job may be to encourage her to cooperate, and help her do the assigned exercises. One favorite exercise of the elderly gentleman for whom I provide care was the passive stretch, where he was to lie on his back, bend his knees, and allow them to fall first to the right, then to the left, without lifting his shoulders from the bed. I was to "help" push the knees toward the bed while stabalizing his shoulders.