Brion McClanahanI’m sorry but I don’t know much about the conflict between Texians and Texicanos.
As to your other questions, yes, there was a push immediately after Texas gained its independence to be admitted to the Union, but there was substantial resistance in the United States to it, mostly from the North, so Texas was in limbo for 9 years. Once Polk was elected and partly on a plank to annex Texas, the issue became settled and Congress annexed it through a joint resolution. Tyler gets the credit, but Polk’s election sealed the deal.
I am not sure about the statistics behind your last point, but several years ago a friend of mine wrote a great article, not available online, about what an independent South would look like and Texas certainly has a large and vibrant enough economy to be independent, as do most States in the Union today.