The answer is no, nuclear weapons are not nearly powerful enough to do the job.
Anyway on the nuclear idea, in detail, see my What is the common scientific opinion about Elon Musk's plan to nuke Mars' poles to accelerate the creation of an atmosphere?
What we can do much more easily is to create habitats in free space or domed cities, or build settlements in the vast lunar caves if they exist - they might be kilometers in diameter and over 100 kms in length if the Grail data is indeed evidence of caves. I think we need to start small, first self contained closed habitats, then maybe larger habitats and caves, Stanford style toruses and there’s enough material in the asteroid belt to build habitats for a thousand times the land area of Earth.
However, Earth remains by far the most habitable planet in our solar system and will be no matter how badly we treat it. There is no way we are going to make it as uninhabitable as Mars, as that would involve removing most of its atmosphere, all its oceans and most of the ice sheets too, and Earth would still be far more habitable than Mars even after all that. And much of Earth is unoccupied sea or deserts.
As Sagan said in Pale Blue Dot
"The Earth is the only world known, so far, to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment, the Earth is where we make our stand."
And despite all that has happened since then, I don’t think any of the ideas for humans to Mars make it remotely as habitable as Earth. And actually surprisingly perhaps, in many ways the Moon is a more suitable place to send humans. It’s far more “habitable” than Mars in many ways when you look at it in detail, at least up to populations of thousands, and maybe hundreds of thousands or millions of people.
I think we are at a similar stage to the early adventurers who discovered Antarctica. Now we have thousands of people living there semi-permanently. But there are no ideas to colonize Antarctica although that would be far far easier than colonizing Mars or the Moon. I think that we should do the same in space, explore, go as adventurers, and find out what it is like there first. Whether we colonize would be for a later decision.