I am fairly sure that "not being granted" means not without a hearing. Much of this depends on which county court you're in, and even sometimes which judge. They have preferences.
There is always a way to try to "undo" something done in court, but it takes more than just changing your mind. With children involved, there must be both a "material change in circumstances", AND the proposed change would have to shown to be "in the best interests of the child". Being a fickle parent with a changeable mind is not enough, and if a parent shows up at a hearing and gives face-to-face consent to terminate parental rights, it is very, very hard to reverse that on the grounds of something like "unfair". . . without something truly compelling like video of some dear family member being held at gunpoint under threat of death while the hearing was going on....
TPR is almost always total--no visitation
rights. After all, that adult is now considered NOT a parent, regardless of biological reality. Parentage
is more about the relationship between people than the biology, in the eyes of the law.
And yes, TPR = no more child support. Because of that financial "incentive", some judges and the law in general are cautious about these decisions.
Typically, the custodial parent
files for TPR of the other parent, based on some unsuitability of the parent, long-term imprisonment, lack of visitation for years, or even huge personality conflict sometimes. But it must be shown to be in the best interests of the child, regardless of what the other parent thinks about it. TPR happens with the other parent's cooperation, and also over that parent's objections.
Just beware, and perhaps get the two fathers "committed" to the idea by getting provable evidence of what they have said on the subject. Sometimes people lie up a storm once they see their "maybe it would be better for Tommy if I. . ." statements put in print and sent to a judge.