You should consider it's much easier rich people to deal with the fallout from climate change (or living in a failed/failing state for that matter) than for poor people. Plus they often have interests in the things that are causing the issue(s) in the first place. Additionally, the children argument is probably the most powerful, but they would probably expect their children to be rich too. All in all I'm doubtful the arguments you are providing have any effect.
I think there is a level of working class poor where it hardly makes a difference what goes on to the world around your life as you are working paycheck to paycheck with much of your available time regardless. How worse it could get doesn’t look appreciably different than how bad it can get already.
A little higher up the economic pole is who stands to lose the most. Those are the people who will see actual quality of life reductions and not be able to afford to return to old norms.