Texas awards custody based upon what it deems the best interest of the minor child. If you can prove the mother "unfit", and yourself to be "fit", presumably you would gain custody. That's a fact-dependent analysis, though, so I cannot state either that the mother would be found "unfit" based upon your suspicions, or that the court would find your suspicions to be a sufficient basis for modification of custody.
If you are truly interested in obtaining custody, you should consider getting the help of a local family lawyer who handles child custody disputes.

