Re: Taking away an incarcerated parents rights.
I cannot tell you Florida law, but after you move to Texas, you would be requesting a termination of parental rights in Texas. The courts do not favor termination of parental rights, but will do so for the best interest of the child with the proper evidence. The court will be much more likely to do so if the father agrees to it. If your ex is willing to sign a voluntary relinquishment of his parental rights, the process will go much easier. The main reason the judge might feel it isn't in the child's best interest is that after termination, the father is no longer responsible to pay child support. However, if he hasn't been paying anyway when he had the ability to do so (before he was incarcerated), that is grounds for involuntary termination.
It is very important to proceed carefully as there have been cases where the termination was done improperly and then later on appeal, the case was reversed. You should definitely hire an attorney to do this for you. A petition will be filed and served on the father, and he will be asked to file an answer or sign a waiver and voluntary relinquishment. The evidence must be presented to the judge, with an order prepared for the judge to sign.
Alternatively, you might seek sole managing conservatorship with supervised or very restricted visitation rights to the father. That way, he would not be off the hook for child support.
In a termination suit, the court will consider that the father did not provide support or care for the child for 2 years or more, and that he was convicted of a crime (criminal conviction alone is not enough to support termination).
If you need an attorney in the San Antonio area, call my office at 210-655-9090.