Hopefully he will re-surface in a few days - most do. But even if he does, your daughter obviously needs to go to court and get a judge to sign some legal paperwork regarding his visitation and custody arrangements.
Please don't wait to go to the TX A G office. This is a very small baby and you will be waiting months to access their free services. I don't think that you want to wait to access their free services.
I recommend that your family gets some money together and hire a private attorney. I don't know who the hospital is referring you to - probably a local pro bono service -- but most are over-whelmed with requests for assistance. If you were referred to Houston Volunteer Lawyers (713-228-0732) you will possibly be waiting for 6 months for an attorney - I assume you don't want to wait that long.
You can look on my website (www.familylaw4u.com) or my blog (www.houstonmediator.blogspot.com) for some pro bono sites in the Houston area. You can call around for free services -- I think you will be disappointed at the long wait lists.
Houston has many fine family law attorneys. Look on this website for an attorney.
Many attorneys offer free consultations. So call around and find one that will work with you on payment plans. Unfortunately it appears that you are going to have a complicated case. Any experienced attorney will know how to get him served with papers to get him in front of the judge and get this case moving.
Please don't put this off because you don't have the money. The longer he has the baby the better the chance that he will be granted custody of this baby. Texas is gender neutral regarding custody - even of such a small baby. However, it is not good that he took a breast fed baby away from the mother. No Harris County judge will like that he did that. However, you did not elaborate as to the reason why the mother is hospitalized? That might be extremely relevant.
I would be on the internet tonight looking for attorneys to call tomorrow morning...
Fran Brochstein has over 20 years legal experience & enjoys educating the public about Texas laws. She is a full-time family law mediator in the Houston area. If you found this answer "helpful" or "best answer", please select the button to show your appreciation. Please understand that this is not a personal consultation and in no way creates an attorney-client relationship. You are strongly encouraged to consult with an attorney in your county in person about your specific legal problem. You can contact her at 713-805-9591 - 7 days a week - her personal cell phone.
If she is in the hospital sick, then not much you can do until she gets better, father has equal standing to child as the mother. With babies, most judges favor mom, but mom is in the hospital. When she gets out you will need to file divorce and ask for temporary orders to get the child back.