I repeat, what other government? If it was legally doubtful, and made no attempt to establish its legitimacy, we can not recognize it as a government.
As to your concern about "your government" allow me to turn it around on you. Would they not have been derelict in their legal, moral and sworn constitutional duty to allow a legally doubtful regiem to assume control over 40% of the nation's territory without offering resistance?
I know damn well I'd be calling for impeachment if that were to happen today.
What would you do?
I believe the Confederacy as it existed prior to Lincoln's provoking the secession of the Upper South by resisting the secession of the Lower South occupied nothing close to 40% of the territory of the U.S. As a matter of fact, I suspect the Lower South, by itself, could not have made a go of it, and would eventually have sued for readmittance to the Union. Without a war. When the Upper South refused to secede, Lincoln won a great victory, which he then proceeded to throw away. All of this is not just my opinion. Seward thought the same at the time.