This may be just one of the popular myths going around, but as Texas joined the confederacy, it support came mostly from white Anglo settlers. the German settlers of the Hill Country were almost unanimously anti-slavery(*) as were most of the hispanics. Both populations were subject to often violent intimidation campaigns by the Texas Confederates, up to and including mass lynchings.
Sam Houston himself was reportedly also opposed to the Civil War and if my memory serves me right even resigned rather than have to sign Texas' declaration of secession.
May be, after the peace, the complete US legislature decided that Texas was simply too big of a state and decided to split it into an eastern and western part in order not to have it dominate postwar politics by its sheer mass.....
(*) The one reception standing out is the town of New Braunfels because of some previous experiences there was one thing the Germans there hated more then slavery amd that was militant abolitionists from the North running havoc in their streets.