The application is sent to the Service Center of the USCIS and if Texas is the one that has jurisdiction over your place of residence this is where you'll send it, but if there is a need for an interview, the interview will be held at the local USCIS office (in Alabama).
As for the supporting documentation, send in as much of it as you have and can send. Certainly mention your child and send in a birth certificate of the child. Beyond that, send pictures, copies of utilities bills, lease/mortgage, insurance, car registration, credit cards, investment statements, bank statements, income tax returns, etc.
Please let me know if you have any additional questions or if I may be of further assistance to you in this matter.
Admitted to practice in CA, AZ, IN and OH