What would be our remedy to adopt our grandchild legally?

I am not sure what "benefits" you wish to apply for, and that is something you will want to discuss with a local attorney. You state the parents "signed their rights" over there are three ways to do this in Nebraska: 1) temporary 6 month Power of Attorney in the appropriate form allowed by law; 2) guardianship through the Probate Courts in which the parents consent to court appointment and supervision; and 3) adoption, in which the parents forever terminate and relinquish their rights and the Court enters an Adoption Decree that creates the legal relationship as if the child had actually been born to you. First, having the power of attorney is the weakest of these, but even just the POA would allow you to apply for benefits and to exercise decisions for doctors/school, etc. The POA does not change the parents' rights, but it does grant you additional rights that only a parent would normally have (including the benefits). These expire every 6 months and they are revocable at the will of the parent. Guardianship is a little more strong. It does not terminate the parents' rights, but it vests those rights in the guardian and the parent would need to come back to court in order to terminate the guardianship. This is an ideal vehicle if it is likely the parent at some point will be able to parent the child and it may be desirable to return to a normal family organization at some point. Guardians can do everything the court allows them to do, and generally have all parental rights including applying for and using benefits for the child. Adoption is forever and final and the child would have the same legal relationship to you that your biological child/children do. It also forever terminates the relationship between the child and the natural parents. You really do need an attorney in order to do anything more than a temporary POA, and I would advise you to speak with an attorney at your earliest convenience to discuss your specific situation. Best wishes.

You have to file a petition for adoption and obtain the consent of the natural parents or have their rights terminated. I am not sure what benefits cannot be received without an adoption. Most times, obtain a guardianship will allow the child to be covered on your health insurance and for you or the child to receive whatever benefits the child could receive with an adoption.