Neither the US Congress, nor the United Nations, have any jurisdiction over anything outside LEO (Low Earth Orbit)
You have de-facto jurisdiction wherever you have the power to assert it.
The American Revolution was about 150 years in the making --- population in 1776, around two million, any disruption in foreign trade wounding, but not fatal. Coastal cities vulnerable, but any penetration into the interior likely to end in disaster. (Saratoga)
The out-world colony for the foreseeable future will be and must be self-sustaining in the sense that it is in no immediate danger of running out of food or air. But it will be small and fragile --- in no position to cut its ties with the earth.