I don't think there is any one correct answer as everyone deals with hardship and grief differently. You have to do what's right for you. I'm a coach and one of my athletes Dad had terminal cancer his senior year of high school/freshman year of college. Somewhat similar to you, his mom wanted him to stay local but his Dad wanted him to go to his top choice in colleges which was about 4 hours from home. For him, school and especially his team, were really important as it was an escape from all the sadness he felt when he was at home, which was overwhelming for him. For him, I feel that not being in school would have made it more difficult. However, this was high school and not PT school and he was also younger than you.
Regarding PT school, during the first two quarters of the grad program I was recently in, I both took and was in all the same classes as the first year PT students, and while it was a lot of work, personally, I didn't find it to be overly difficult. In fact, I found undergrad harder due to my being in a Varsity sport and having much less time, although it could also be that I'm older now and know how to study. However, there were some students who really struggled, but there were also those who had an easier time of it than myself (I'm not saying it was easy!). One of the PT students had a family and juggled his time between them and school, and another of my classmates mom had terminal cancer. Both were able to make school work and did fine. It really varies on the type of student you are as to how difficult and time consuming school will be and as to how you handle hardship.
As one of the writers mentioned, I think seeing a counselor with whatever decision you make is beneficial. In fact, you may want to think about talking to a counselor now and then make your decision as they're probably going to give you better advice/help you think this out, than we might be able to. It sounds like you feel guilty either way, and that's something they can help you with as well. Good luck with your decision and I wish you and your family the best.