what disease would cause someone to shake and lose the ability to write?

So my mom has early-onset Alzheimer s disease and she recently is having problems with her motor functions where she can t write she is sometimes shaky and clumsy she also has problem when she is in front of a mirror she will put makeup on the mirror and not her face....is there any other disease that can cause stuff like that? (we were told (not by a doctor) that she looks like she might have Parkinson)