I find our different ideas really interesting. I hear you that it's repugnant that the well-off would be able to live the same lifestyle while the poor would be hurt. I don't like it either. There are a few ameliorating or redeeming factors, though--and I'm not an economist so please know that a more knowledgeable person would make a stronger argument, but the hero you need isn't part of this thread.
First, it might not happen the way you expect. Traveling by plane costs so much energy that it might take a bite out of the travel budget of even the rich. Not Bill Gates or Taylor Swift, but I suspect the very richest people are a small proportion of travel. And few rich people actually enjoy blowing money. The social pressure (of spending an extravagant amount on travel) would also push the rich to more often fly on commercial flights instead of private.
Next, there is a "minimum fair" cost of emissions. It's hard to say what that is, but if I'm being ethical in the "do no harm" sense, I should pay the cost of energy production plus necessary profits (the market rate) plus the cost of harm: environmental, warming, rising coastlines--everything. The cost of harm is hard to calculate but if politicians even started thinking about this, it would be a start. Imagine a carbon emission fund, a methane emission fund, and a XX greenhouse gas emission fund. Gas purchases would include payments to the first fund, and it would be dedicated to environmental repair in all the ways you'd expect. (The last fund would be more around ozone layer repair than the first two.) The net harm would be zero. This is called a Pigouvian tax, but I'm not sure if it has ever been implemented in a totally correct way.
Banning emissions by legislation would also have unintended consequences. Even very complicated legislation does not take care of edge cases. Say you made air freight impossible or limited the number of times a person could fly per year. Your legislation would not take into account how much I need an urgent package or how badly you need to fly to see a sick relative (despite recently having traveled). But if the harm were built into the cost, we would be able to make that decision for ourselves. The $100 shipping or $3000 flight might seem like a bargain based on how much we needed it. But if you make it illegal, all that extra value (how much I need the package / how much you need the flight) is thrown away.
Finally, the rich being rich and the poor being poor is sad. I don't like it. It doesn't feel fair. This is a topic that I've heard elegant arguments about which I can't reproduce, but suffice to say I'm not aware of any way to improve the situation that doesn't involve horrid unintended consequences--except perhaps a Pigouvian tax. Theoretically, I'm interested in whether solving collective action problems and reducing transaction costs could give more opportunities to the poor, but I have nothing to share on that yet.