You can seek a divorce in TX for adultery which will also give you an advantage when the property is divided up. Adultery is hard to prove so your petition should also state insupportable which means you can't stand to be in the marriage anymore.
In Texas, adultery is a fault ground for divorce that may allow for an unequal division of the community estate. The bigger issue is your husband's drug use with the potential of further waste of the community estate and the effect it will have on his ability to have any opportunity to see his children (though from your question that does not appear to be an issue). You consult a family lawyer in your area to make sure any divorce petition you file contains the necessary pleadings regarding protecting you and your children and the community estate.
Yes, you can sue for divorce, and take care of custody and support issues at the same time. Adultery would probably work, if he is living with her. You may even be able to get him to pay retroactive child support, but you should talk with a good family law attorney in your area, as some of these issues are complex.
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