Calling it School of Choice is kind of deceiving. If it's the same as it is in Miami, here it works. You are zoned for 2 or more schools. You "choose" in order of preference which of these schools you would like to attend and then submit your choices. There is a behind the scenes process and then you are notified, which of your "choices" you received. You can appeal the decision if it is not what you wanted, but I'm not quite sure how that part works.
You mentioned your daughter was in the Gifted program in Texas. Was she officially tested? If so, then check to see if the state will accept your daughter's test results from TX. If not, you will need to have her tested here again if you want her in the gifted program again. I recommend you go the route of private testing and not do it through the schools. If she tests gifted, then you may have some options regarding schools. I don't know all the details (call your counties Gifted or Exceptional Education office for more), but I believe you have a right to choose what type of gifted program your daughter is in (full-time, part-time or pull-out). If the school you are currently in, does not offer the type of gifted program you want, then you have a right to put her in a school that does. I believe this is on a space available basis, but it could open up your options.
Good luck. It is definitely a challenging system to work through.