And it happened to me too, my son was 1 and 1/2 year old when he was chocking on a bottle cork he 'stolen' from me,
He was lucky to be on my knees when this happened, because basically when one gets chocked, he can not say anything... no noise would come out, the first thing I did when I saw his condition was trying to grab the 'thing' that choked him with my fingers, but did not manage to reach it, the next thing was hitting him on the back, that did not help either... I took him upside down holding his feet and hitted him again and bit stronger on his back, and the cork jumped out.... I must admit that his cry that came instantly after was the sweetest sound I ever heard in my life.
I do not think there is any magic solution, one needs to watch his kids as as possible.
I wish the best to the family, and hope they would recover fast, there is nothing they could have done to prevent this, it can happen to anyone and any time.