I`m so sorry about your aunt.
First of all why aren`t her children helping out???
Second ... as much as you may love your boyfriend ... If i had a man who said that to me, about breaking up and long distance relationships don`t work... I`d be furious with him and i would end the relationship it right now.
How close you are to your aunt, If you are close then you have to go, maybe you won`t be there for 7 week, and your right ... it isn`t long, could you live with yourself if you didn`t go and something happened.
I would be ashamed of your boyfriend if he was a relation of mine, not going to see his grandfather when he went through all of the chemo.
As much as it may hurt you if your so called boyfriend broke up with you, I would go, but it`s your decision.
Long distance relationships do work, I met someone on the internet, I lived at one end of the country and he the other, we are now married.
you deserve much better than someone who is trying to blackmail you into doing what he wants.
What ever you decide, good luck.