Mouse options for accessibility

My grandmother is getting to a point where using a computer is becoming very difficult. Her hand tends to shake, and using a mouse or trackpad in particular doesn't seem to work very well. She currently has Ubuntu on her desktop, and a chromebook as well.

Does anyone have any input suggestions for mouse replacements? It's funny, but I think an old-school arcade style joystick moving the mouse slowly with a few buttons would do the trick, but am having trouble finding an out of the box solution for this. Does anyone have any suggestions? I know it should be possible to use a custom input controller for an actual arcade style joystick (8-way). However, an existing solution would be preferred.