This is quite the post, where space lawyers think the law isn't possession and force projection. Without force behind a law, they are just words. Mars will be independent the moment they no longer need Earth for resources, decided by whomever governs Mars.
But earth has the bigger fleet, not as advanced as mars but still, and the belters have something to say too.
Good luck with that in your fragile vacuum vessels.
It will just be called the Compromise of 2057 and all legal claims and military presence will be dropped and recalled.
Worse has happened before.
Yeah, and that will happen... if and when a series of extremely challenging technological and social hurdles are crossed. Especially, the ability of humans to live on Mars for any extended period of time is doubtful given the limited gravity[1]. Mars is going to need influx of humans for a long time, hopefully with them also leaving well compensate. "Mars ain't the kind of place to raise a kid"[2]
[1] https://en.wikipedia.org/wiki/Colonization_of_Mars
[2] William Shatner
Either you can enforce your space law, or you're irrelevant. (But they may in fact be able to enforce it in Earth court. We'll see.)
A colony on Mars would have to adapt fast to the challenges of that environment, they can't be expected to wait for Earth bureaucracy to decide if they are allowed to act. In fact, the colonization of Mars should be modeled after the colonization of the American Continent; everything that was done then will be repeated on Mars, with the exception of genocide.
Or even sooner, when the Martians are backed by some earthly sovereignty that gains enough from the cooperation to really don't give a damn about who is in charge over there.