I’m certainly sorry to hear about these aspects concerning the priest and godfather associated with your daughter’s baptism, and if I were in your shoes I would likewise be feeling very hurt and let down. But the only reason a person should undergo a second baptism ceremony is if the initial baptism is determined to have been invalid (or there is serious reason to suspect that it was). In such a case, what is called a conditional baptism may be permissible. All this is found in Canon Law as follows:
Canon 845 §1. Since the sacraments of baptism, confirmation, and orders imprint a character, they cannot be repeated.
§2. If after completing a diligent inquiry a prudent doubt still exists whether the sacraments mentioned in §1 were actually or validly conferred, they are to be conferred conditionally.
In order for a baptism to be valid, there must be proper matter, form and intent. Matter refers to the use of water, and form refers to the Trinitarian formula spoken by the minister (i.e., that the person is baptized “in the name of the Father, and of the Son, and of the Holy Spirit”). In addition to this, the minister must have the intention of baptizing the person in accordance with what the Church intends. Note that the moral character of the minister is not a factor for the sacrament’s validity. Unless there was an issue with the matter, form and/or intent of your daughter’s baptism, no priest or deacon would be permitted to do an additional baptism ceremony for your daughter because a re-baptism would be invalid and, from a theological perspective, considered an abuse of the sacrament (as a side note, I’m using technical catechetical language here; I fully understand that your desire is not to abuse a sacrament but rather one which stems from a mother’s love for her child).
In terms of godparents (a.k.a., sponsors), Canon Law states:
Canon 872. Insofar as possible, a person to be baptized is to be given a sponsor who assists an adult in Christian initiation or together with the parents presents an infant for baptism. A sponsor also helps the baptized person to lead a Christian life in keeping with baptism and to fulfill faithfully the obligations inherent in it.
Therefore, even though having a godparent is an important aspect of baptism, it is not required for the sake of validity (which is why the above law states “insofar as possible”). Therefore, if it is determined that a chosen godparent was not really up to the task (for whatever reason) then this does not effect the validity of the baptism in question. Moreover, although most people have two sponsors (a godfather and a godmother), Canon Law only specifies the selection of one (as you can see above in Canon 872). The selection of a godfather and a godmother is treated as an option (and is mentioned in Canon 873). My point here is that even though you have come to regret the selection of your daughter’s godfather, it sounds like you are happy with her godmother, so your daughter still has someone to properly fulfill the ongoing role of a baptismal sponsor.
To better illustrate what happens in the spiritual order of things, I sometimes like to make a comparison in the physical order of things. Let us say that a young child needed an operation to deal with a serious medical problem. The operation was carried out by a surgeon who was assisted by the child’s pediatrician. The operation was conducted in accordance with official medical procedures and the problem was corrected. Later the surgeon was imprisoned for sexual assault and it was shown that he had been leading an immoral life for several years. In terms of the pediatrician, he did not seem to share the values of the child’s parents, and did not really seem truly concerned with the child’s welfare.
Based on these things that came to light, should the parents seek to have the child undergo the same surgery again? No, because neither the sinful character of the surgeon nor the problems with the pediatrician had any effect on what happened in the operating room; the surgery was still a success and the medical problem was corrected. Comparing this to the baptism of your daughter, the medical problem is Original Sin, the operation is baptism, the surgeon is the priest and the pediatrician is the godfather. There is no need for another surgery, nor is there a need for another baptism ceremony.
With all this in mind, I ask you to please consider the following recommendations:
Always keep in mind that the reason why the sinful natures of ministers do not effect the validity of baptisms is because Christ is the High Priest who works through them. Going back to my surgery example, there was another surgeon doing the operation - Jesus Christ. Christ is the one who baptized your daughter (working through the ministry of the priest).
Focus on the godmother being active in your daughter’s life as her baptismal sponsor. If her godfather doesn’t want to shape up and have an interest in doing this then it’s his loss.
Set your sights on eventually having a beautiful confirmation celebration for your daughter. Her godfather need not have any involvement in this. Your daughter’s godmother can also serve as her confirmation sponsor (Canon 893 § 2 even states that such a thing is desirable), or you can choose someone else, such as the other uncle you mentioned (assuming that the desired sponsor also meets the standard requirements).
For more information on this topic, I recommend reading Fr. William F. Wegher’s Godparents and Sponsors: What is Expected of Them Today