Frankly, I think that since no one has come forward the following is true:
Baby Grace's immediate parent/partner were local or within a day's drive. Houston is a strong possibility just because of the number of Wal-Marts/Targets and closeness to Galveston. You can't drive around much without being aware of how close Galveston is. However, the other locations--even Louisiana--are possible as well.
The extended family is deceased, dysfunctionally separated in geography, and given Baby Grace's age of 2-3, not necessarily aware of her birth or appearance even.
The perpetrators are either the parent/and partner, or single parent acting without knowledge of the other parent. However, I really do believe this is an act of stepfather/boyfriend and complicit mother. The fact that she was violently injured and dumped points to an abusive partner, but the clothing condition points to someone who picked out clothes with care for her.