There is a different process called "step-parent adoption". Look for that. Usually just requires notice and assent from the biological parent who is giving up parental rights. You do not need an attorney just be sure to file the approrpriate forms. The court staff will not tell you what forms to file (they can't, = the practice of law and that is where you need a lawyer). Some courts have legal service offices that help people wanting to represent themselves. Jurisdiction is the county where your daughter lives. That the original agreement is in Delaware is not relevant for that issue.
Start with a trip to the courthouse. Look for a help or info desk. Let them know what you want to do and ask about any legal services that can help. Some counties even publish self-help guides which walk you through the forms. Sometimes a court's website can give you all the information you need.
This is a very doable situation. I wish you all well in getting to your results.