Terraforming your own planet to make it less habitable while trying to terraform a hostile planet to make it more habitable seems like an odd way to do things.
It doesn't have to be either/or. But politically, the odds of an unsuccessful Earth creating a viable Mars colony are somewhere very near zero.
That's a remarkably good suggestion. Only answer I can come up with: It'd be really really hard to declare independence from whatever nation's land the bubble was sat on. Float & anchor it in international waters? Problem solved!
It doesn't have to be either/or. But politically, the odds of an unsuccessful Earth creating a viable Mars colony are somewhere very near zero.