Transferring PhD programs due to parent's sickness I am a PhD student that has just started my third year in a scientific field. Since I have started my program, my mother has been diagnosed with a serious form of cancer. It has recently gotten worse and I am worried sick. I am considering applying to another PhD program that would be much closer to home.

This other department would also meet my research interests better than the current one. I have not been super excited about my current research so that is a factor in my consideration too (although I was not seriously considering leaving before this happened). I am much better aware of my research interests now than when I first applied to graduate school, since my undergraduate degree was in a different field.

I should mention that the program that I would be applying to is generally higher ranked, although my current one is respectable too. I have not applied to that department before. I have four publications, two first-author papers in good journals and one in Science (not first author). My advisor is very well-known and is very sympathetic to my situation. I have not discussed the possible transfer yet and although they would be saddened if I left, I'm sure they would write a great reference letter. My grades in the PhD program are not outstanding since I was mostly focused on research. I will likely have my master's degree by the time I would be applying in the winter.

I know transferring PhD programs is generally not easy, especially when it's to a more prestigious department, and given that by the time I would start I will have completed 3 years at my current department. But considering my situation and my publication record, how understanding would an admissions committee be? Does anyone have any experience with a similar situation or advice?

Thank you so much.
Advisors are humans too (at least most of them). Most would be willing to think with you to find creative solutions. Maybe you can stay with your old institution, but arrange for you to visit the new institution. I my old institution a couple of months in another institution was mandatory. So you can keep the progress you have made and still spent some time closer to your family. Maybe, you and your current advisor can arrange for someone from the other institution to become your co-advisor. This might enable you to regularly travel back and forth as part of your normal work, and combine that with family visits. 

If people are willing a lot is possible, and in situations like yours a lot of people are willing. So my advise is talk to your advisor. Don't limit yourself to that new institution. Your primary aim is to spent time with your family, and the new institution was one possible way of achieving that. Maybe your advisor has other ideas on how to achieve your aim that work out better.