I would absolutely not go on the trip. Even if I had my mom or brother taking care of the animal I would not be able to go enjoy myself. If the cat is really THAT sick I would let him go and be free so I could have a peace of mind while on my trip. Sure I'd be very sad, but I'd know my kitty wasn't at home suffering in pain.
It makes me sad to think this kitty may pass on his own without his family around.