There is an interesting Facebook discussion about a Gladney adoptions. A poster googled six flags and adoption and this popped up (Six flags Arlington supports the Gladney Adoption center). Logan's aunt is going to call it into Logan.
http://www.facebook.com/group.php?v=feed&story_fbid=306550777296&gid=251236072296
Anyways, the FAQ section is interesting wrt father's rights (snipped and BBM):
"Reader Questions and Answers
Q: The mother and father had already broken up before she knew she was pregnant. The father wants to raise the baby with shared custody, but the mother wants to give the baby up for adoption. Can the father stop the birth mom from giving the baby for adoption?
A: Each case is handled on an individual basis. If the birth mother is interested in adoption, she would need to call us so we can get more information to make a better assessment.
Q: Do I have to tell the dad before I give my baby up for adoption?
A: Gladney would need more information about your situation before an assessment can be made. Please feel free to call 1-800-GLADNEY (800.452.3639) and ask for an admissions counselor so we can learn more details about your specific situation.
Q: I want to put my baby up for adoption. Where do I start?
A: The first step in planning adoption is to fill out a background information packet. Call 1-800-GLADNEY (800.452.3639) and ask for the admission department and they will guide you through the process.
Q:
Can you place your child up for adoption if your child is over 6 months?
A: Yes, we can help you plan adoption if your child has already been born. You'll need to call 1-800-GLADNEY (800.452.3639) and ask to speak with an admissions counselor so they can explain your first step in making an adoption plan."
Edit: Something else I read on their site, they are licensed to do home studies in :Gladney is licensed to complete home studies for families in Texas,
Arizona, Kentucky, New York, New Jersey, Pennsylvania, North Carolina, Oklahoma, Arkansas, and Louisiana. POssible TS connection?
http://adoptionsbygladney.com/html/pregnant/faq.php
LAST EDIT: I don't see much connection to San Antonio, but definitely the FAQs show they have some flexibility with father's rights.