While it is true that the Treaty of Annexation bringing Texas into the United States contained clauses that might allow the Republic either to secede later or to divide its territory into four separate states, the legal argument is that Texas' readmission into the Union after the Civil War supercedes the clauses of the original Annexation Treaty. Quite simply, when Texas applied for reinstatement after the Civil War, the original annexation agreements were supplanted by the readmission agreement.
The important question as far as Texas is concerned would be "was the original Annexation legal?"
I have a copy of the letter from Anson Jones to the Texas Senate "announcing" that the treaty annexation was a "done-deal" despite the fact that there had been no public vote by the Texians approving such annexation. The deal was cut between Anson Jones (2nd President, Republic of Texas) and James K. Polk (President of the United States) with congressional approval in both the United States and the Republic of Texas.
Bear in mind, that territorial admission for statehood into the United States required petition and vote by the populace of a given area while the treaty annexation of a sovereign nation required only the votes of the government of the Republic and the United States. Whether the Texian populace would have approved Annexation is a moot point -- they had no opportunity to vote. It was done in the halls of the capitols of the United States and the Republic of Texas. The politicos made their decisions without public vote.
The annexation of Texas is the only case wherein a state was created without a public petition for admission and subsequent public vote on the question of Statehood.
As to the matter of secession and reannexation -- Sam Houston was a vocal opponent of secession at the advent of the Civil War. His arguments were pragmatic in nature rather than emotional. He expected the Confederacy would lose and saw no compelling reason to join a lost cause. Houston's arguments were fairly well-received at the time. He argued that the Civil War was an American problem that Texas should abstain from joining.