This is from University of Houston's website:
"Dependent students may base residency on a parent or court-appointed legal guardian. The parent or court-appointed legal guardian, however, must have resided and established domicile in Texas for 12 consecutive months."
University of Houston : Residency Requirements
If your plan would be to pay out-of-state the first year, and then switch to in-state, I would call admissions and make sure that's possible. Make sure they know you would be living with your parents over that first year, and that when your parents and you have lived there for 12 months you hope to be paying in-state rates.
Usually public colleges will not let your establish residency just by virtue of being in the state as a student, but since you're parents will be living there it may be different.
Or else you could move with your parents but put off beginning college for year.
Call and ask!