How do I get a letter of custodial-ship to show that I am my child's legal and only parent in order to obtain an inheritance?

Because the payment cannot be made to the child, the child needs a guardianship so the court monitors the money paid and you are under responsibility to turn it over? the to child when she reaches 18 years of age. This is done through court setting up the guardianship. You will need an attorney to help you do this. Although the insurance company attorney is sometimes pressed into doing it for the company with your cooperation.

This appears to be a probate question. You will want to inquire with an attorney who advertises his/her services for wills, estates, and probate.

Because the child is a minor. The court and the insurance company want the beneficiary, the child to get the inheritance, by making you go through the courts, the money will likely be put into the hands of the court for the child, not in a bank account controlled by you alone.

Because the money has to go into a separate account for your daughter. If you want to do this right, you need to set up a conservatorship with the court allowing you to take the money in and then spend it only on her.