Our duty to our great-grandchildren is to figure out how to get through the 21st century without a collapse. We have all the rest of history to get through, but we cannot even imagine what the problems and opportunities of the 22nd century will be, so let's concentrate on what would constitute interim success by 2100.
Interim success in 2100 would be a world in which a recognizable descendant of the current civilization is still thriving. The global population might be heading back down toward the current 7 billion by then, having peaked at several billion higher, but it won't fall faster than that unless billions die in famine and war, so it must be a future that can sustain a very big population.
Unfortunately, the way we are living now is not sustainable. We have taken too much land out of the natural cycles in order to grow our own food on it. We are systematically destroying the world's major fish populations through overfishing and pollution. We are also driving most of the larger land animals to extinction.
This is a "six-planet" civilization: It would take six Earth-like planets to sustain the present human population in the high-energy, high-consumption style that is the hallmark of the current global civilization. Not all of the 7 billion have achieved that lifestyle yet, but they all want it and most of them are going to get it.
That's the real problem we must solve if we are to reach 2100 without civilizational collapse and a massive die-off of the human population. All the other stuff we worry about, like global warming, ocean acidification and the "sixth great extinction," are really signals that we are not solving the basic sustainability problem. Nor will we ever solve it by just using less energy and eating less meat. Not at 7 billion plus, we won't.
So we really have only two options. We can go on in the present patchwork way, with a bit of conservation here and some more renewable energy there, in which case we are heading for population collapse through global famine, and probably civilizational collapse as well because of the attendant wars, well before 2100.
Or we can try to float free from our current dependence on the natural cycles. Use the scientific and technological capabilities of our current civilization to reduce our pressure on the natural world radically. Stop growing or catching our food, for example, and learn to produce it on an industrial scale through biotechnology instead.
Just achieving food independence would greatly reduce our vulnerability to climate change, but we need to stop global warming anyway. Otherwise, much of what we call "nature" will not survive, and half the world's big cities will be drowned by sea level rise.
Given how much excess carbon dioxide we have dumped into the atmosphere already through burning fossil fuels, that will probably require direct human intervention in the climate system: geo-engineering, in other words. We must also stop burning fossil fuels and move to alternative sources of energy as fast as we can, but we almost certainly won't move fast enough to avoid geo-engineering.
This civilization is the distilled essence of a 10,000-year human fascination with technology. It will live or die according to its ability to solve by new technologies the problems it has created.
If we want our great-grandchildren to be alive and happy in 2100 we have to start managing some of the planet's systems (like climate) and remove ourselves entirely from some of the others. There is no third option.