Yes - you can file a petition in suit affecting parent-child relationship. You should probably hire an attorney, as you are going against one of the presumptions in family law, that the parent (father) knows best... but on the facts stated, you have a decent chance at establishing yourself as a primary custodian, with the Father having visitation.
This answer is intended for informational and educational purposes only and should not be considered legal advice nor forming the attorney client relationship. This attorney is licensed in Texas.
I would be in the office of an experienced family law attorney tomorrow! The clock is ticking and you need legal representation now!
If you don't have an attorney call PATRICIA BUSHMAN at 713-807-9405. She takes payment plans. I rent space in her office so tell her that I sent you to her. She won't talk to you on the phone so just call her office & make an appointment immediately. She has lots of courtroom experience & her prices are very reasonable for her years of experience. I obviously think she is good or I would not rent space in her office.