Your children will and their children will be fine, but there's big and real chance that they will not have the standard of life you have and certainly far below what they could have. I think that's plenty scary in its own.
What about the children who died in the fires now in USA, in Australia, Floods in India and elsewhere all of which have been worse than ever in this century and the reason being attributed to climate change?
What's at stake isn't the death of the planet, or the death of life, or the death of civilization. All these things are resilient enough to adapt to the effects of climate change.
What isn't resilient enough is our quality of life, which is based on my assumptions that climate change will invalidate. The next generation will thus have to spend their surplus resources dealing with these adaptations, instead of leveraging themselves up into higher and better lives.
Everything lasts forever, until it's over. Extinctions are the norm in Earth's history. There's no reason to think humans are the exception. The fact that humanity has yet to die off isn't much comfort. It's a sample size of 1 species, and by definition we wouldn't even be discussing this if the alternative happened.