I’m asking this because one of my parents are moving to Texas and my other parent is staying back in a midwestern state with a lot of medical schools. Currently, I’m a resident of the midwestern state but my drivers license will expire before I start applying so I’m wondering if it would be a good idea to become a Texas resident because of the match system that they have for instate applicants.
No, they don't really have it better. That's just a common misconception because the TX schools have a tremendous bias in favor of IS applicants, resulting in a 27.3% IS matriculation rate compared to the national average of 21.9%.
So, if you have your heart set on a TX school (and very low IS tuition is a very legit reason!), then you are far better off applying as a TX resident. The rub is that, even with that preference, TX applicants get absolutely destroyed as OOS applicants (5.5% matriculation rate compared to the national average of 14.4%) because schools in other states, both public and private, reasonably believe that TX applicants will want to stay IS if given a choice. Consequently, a lot of attractive applicants find themselves screened out along with the less attractive ones.
This doesn't apply to Harvard caliber rock stars, but the numbers suggest that it does apply to most people (again -- 5.5% OOS matriculation rate!). As a result, even with the strong IS preference, the OOS bias more than counteracts it, and TX applicants had a 32.8% success rate last year as compared to a national average of 36.3%.
So, as
@wysdoc said, if your heart is in TX and you really want to go to med school there, then go for it. Otherwise, moving to TX to try to game an advantage in med school admissions in a few years is far more likely to backfire than work.