I promise you, you'll feel like such a jerk if you don't do this, you skipped out on your grandpa's last remaining weeks so you can spend time to yourself. I highly recommend you sit down and think about this for some time, you gotta think of the cause and effect of the whole situation. If you don't do this, your family might lose respect for you.
Do this for your family and your grandpa, in the end you can say to yourself that you actually did show some compassion. You can also talk to a school counselor about your situation, they might be able to talk things out with you and give you advice on what to do.
I hope everything works out for you.
it seriously sucks.
5 weeks is a little extreme, but if you don't go... at least for a little while, you'll regret it. see if there's any way you can compromise and be driven home early or just come up later.