2 options: 1. "I hope I (will) live to see my grandchildren." 2. "I hope I (will) live long enough to see my grandchildren." "I will never live it down" is a more colloquial way of saying "No one will ever forget that I did it". More commonly, you will hear "I will never live THIS down," because it is normally used as a response to someone reminding you of what happened.

I hope I live LONG enough to see my grandchildren. - The 'long' is important here. "I'll never live it down" always signals embarrassment at a past event. There aren't really any other exact equivalents that I can think of. Other similar options are: "I'll never get over that" "I wanted the ground to swallow me up"

It should be "I hope I live long enough to see my grandchildren." The other sentence could be restated as "I did something so bad that no one will ever let me forget it." (They will keep reminding me about the time I started my pants on fire, or crashed Dad's truck, or got drunk and jumped into wet cement.)