I was in your situation, but as a pre-med doing their post-bacc to get ready to apply to medschool. I was doing a DIY post-bacc which entailed starting over as a freshman (unfortunately). Two years in, my father was hospitalized. Because I was the only child living in the same city, I took a LOA to be at this ICU bedside for close to a year until he passed. Because my father worked 12-15 hour days in the service industry as I was growing up, I rarely saw him and we were not close. However, we got closer as I was doing my PB and would have lunch on his 1 day off per week prior to his hospitalization. The final years I spent with him are memories that I will cherish forever.
Family comes first OP and when you are ready to apply and if a residency program holds a LOA against you because of your circumstances, then it's a program with a culture that you have to think long and hard about joining. Peace be with you, your father, and fam...