“Proving Family Illness: Finding the Best Documentation for an Excused Absence”

My grandmother is in a nursing home due to dementia. However, it’s not in the United States, so I’m unsure how to prove this to my professor. I’m contemplating whether I should lie about one of my parents being severely ill. Could we discuss and possibly provide a doctor’s note together?” 
I’m not sure if a doctor’s note would be considered the best documentation, but it could be included as part of it.
I received an F in this course. So, I explained to the professor that my mental state was shattered due to unfortunate news within my family (My grandma), and also because I had to work two jobs to afford tuition, which led to this outcome… so please help me with this situation. 
My professor told me : 
please provide your “best” documentation related to your family member’s illness. This will help me evaluate your situation in line with our excused absence policy outlined in the syllabus.