Has there ever been such a thing where two distinct legal systems are enforced in separate, geographically defined areas of the states and where the laws are diametrically opposed to each other? It sounds like a very odd deal going on here.
Texas sold that claimed territory to the US government in order to cover its debts occurred throughout independence. Without the sale, Texas would have had to pay for all of its own debts. I'm not sure about the numbers, but it would have taken years to pay it off on its own. (That is consistent with earlier behavior after the Revolutionary wars; states sold their claims to the federal government so that they would take on their war debts). This is double the case as Texas had really loose control over its western sections for years; the lines of settlement were rolled back time and time again. And, seeing how effective Confederate efforts were during the war in the then Arizona territory, they would have probably lost any effective control of the west.
Any West Texas government would be centered around El Paso and de facto would have been free of slavery, even without a compromise That, and the largest chunk of that territory, the New Mexico portion, was not slavery free OTL; it was to be decided by a plebiscite of the inhabitants. If such a thing ever came to pass (as weird as that would be), it would likely have Southerners demanding a similar status in South California as well.
Likelihood of what happens if this arrangement makes it to the war? The Arizona territory becomes that much more important to the CSA as it links South California with Texas. However, South California is pretty much as Unionist as OTL, and any Confederate attempts to take it will have to come from across land. Sam Houston, after failing to keep Texas in the Union, flees to Santa Fe to set up the Texas government in Exile. By 1863, any attempts to go west having failed, Confederate Texas is only managing to hold onto the eastern region where its main population is... and barely at that.
If the war ends early (62/63) then Texas is likely reunited and the two different statuses are dissolved afterwards. If the war ends later (64/65/etc), then the two regions likely will separate and West Texas will take many Unionist counties with it (and will probably get some of the New Mexico territory as well).