The laws of the State of Texas are gender neutral. The laws do not favor women any longer. Obviously the father was able to show the judge that he could provide for the child.
In order for you to gain custody of the child, the burden is on YOU to show why custody of the child should be changed. I assume that his father would contest the change in custody. You would need to be prepared for a custody battle. I assume that you would need to be prepared to spend at least $10,000 - $15,000 for a custody battle. If you don't have this type of money, then I would not bother beginning the battle.
I do anticipate the pro bono (free) services accepting your case. They are too backlogged. I worked at Houston Volunteer Lawyers for 4 years & was an active volunteer with them for many years.
Do not hope and think that any family law attorney will accept your case on a pro bono (free) case because they free sorry for you. Every family law attorney in Harris County receives calls like yours on a daily basis. Many family law attorneys are willing to accept payment plans and to "work" with clients regarding their legal invoices -- but they cannot take a case like yours that will require hundred of hours of preparation and courtroom work for zero pay.
You need to pay the past-due child support. I would not waste your time attempting to go back before the same judge again & try to regain custody until that past-due child support has been paid in full.
However, if an emergency situation arises where your son is in danger, then that would be another matter. If the father is arrested or receives a DUI, then immediately petition the court for custody. You would then have grounds.
So what do you need to do? Save up your money to hire an attorney in case an emergency situation arises. You will need to be able leap into action to save your son. The case will remain in Harris county since your son resides in Harris County. It is irrelevant that you reside n Ft. Bend County.
If you would like to meet for an hour and discuss your situation, I would charge you $150 to discuss this matter and discuss your options.
You need to continue to visit your son and take advantage of all visitation. Do not miss a visit. Keep a record of all of these visits, etc. Have witnesses that can come to court and testify. Live a clean life.
It would also be vital to know which Harris County judge you would appear in front of when you return to court.
If you want a consultation, you can email me at email@example.com or call me at 713-847-6000.
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Were your parental rights terminated? If not, the current order likely gives you some visitation, even if it is supervised.
If the current order does not give you the visitation you want, you need to file a petition to modify. The fact that you are now employed, have a place to live, and transportation should be a basis to seek a modification.
You really need an attorney to help you.