Fairly tricky. You should be able to make the case that you have standing for Custody / Possession and Access because you have lived with "step-son" for the last 6 months prior to filing suit.
I offer free consultations and am quite familiar with family judges in Harris County and nearby counties.
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You have standing to file suit, which means you can get in the game and have a judge decide. But you really need to consult with a local family law attorney who can ask you a lot of detailed questions and then give you an answer better tailored to your specific facts. These are not black and white cases and each fact really matters.
Two other things:
(1) The verbal abuse is coming from somewhere--Maybe problems coping with some stress or alcohol/drug use. See if there is some way to get at the root of the problem. People who start exhibiting this kind of behavior are not always open to the idea that THEY are the problem, so you might need to see a counselor by yourself FIRST and get some advice on how to approach your husband with the goal of getting some family counseling. I say this because I think that step-parent possession and access is a dicey deal and, if you can make your marriage bearable, that will probably yield the best outcome. You clearly want the marriage to work--if only for the kids--so try that.
(2) You would have a clear case to possession and access of the child IF you had adopted the child. If the mother voluntarily terminated her parental rights and you did a step parent adoption, you would have the same rights as if you had given birth to the child. I'm not suggesting you try to do a step parent adoption in the midst of a collapsing marriage--just want to give you an idea of the type of change in facts that would give you more certainty in a future divorce/custody dispute.
I'm sorry things are not going well at home. Good luck!
If you were to file for divorce, this stepchild would not be a subject of your divorce case because he is not a child of your marriage. To modify the terms of the prior order regarding your stepson, you would have to file a suit to modify as a separate case....and unfortunately, in my opinion, it is HIGHLY unlikely that you would be successful.
The only chance you have for obtaining visitation rights to your stepson is to adopt him and then get divorced. And in order to adopt him you would need for the mother to voluntarily relinquish her parental rights to this child. If she does not voluntarily relinquish her rights to the child, then you would have to proceed with an adversarial case to terminate her parental rights. Terminating parental rights is serious business and the courts generally won't do it just because the parent isn't particularly involved in the child's life. Since she does spend a chunk of time with them every year and you have not stated that she has abused or otherwise mistreated the child, I do not see any judge in harris County involunatrily terminating her parental rights if she fights it.
In sum, in my opinion, the only chance you have for obtaining visitation rights is if you play nicey nicey with your husband, you and and your husband file a suit for you to adopt your stepson while you are married, the mother consents to relinquishing her parental rights, the adoption is finalized 6-12 months later, and then sometime thereafter you file for divorce. Of course, as per another contributor's response, the advisability of seeking a stepparent adoption when things between you and your husband aren't good is debatable.