". . . subject only to the Constitution of the United States,"
OK, I understand that part, too.
". . . and the maintenance of our free institutions and the perpetuity of the Union depend upon the preservation of the right of local self-government, unimpaired to all the States."
As I understand it (being no constitutional scholar or lawyer), this means that Texas's status as one of the United States is contingent upon the maintenence of a division of powers between state and federal government. I read nothing here that denies Texans the right to secede.