How do I get legal custody of my daughters without going to court?

In Arkansas an unmarried mother is deemed to have sole custody of the child(ren). In order for the children's father to have custody or even visitation rights he would need to petition the court for paternity and visitation and then receive an Order from the Court for visitation or any other other parental rights he might wish to obtain. Being on the birth certificate does not give parental rights but it will be enough for Child Support Enforcement to seek support on your behalf. At this point you already have sole legal custody. If you are being denied passports you might want to petition the court for an Order allowing you to do so.

In Arkansas the unmarried mother of children has sole custody. If the father has not been adjudicated the father in a court of law, (i.e. child support court) then the mother has sole custody. That being said, for the purposes of a passport you will probably need to get a guardianship or custody from court. The reason being to stop parents from fleeing the country with minor children. So the answer is probably not, unless the issuers of passports will accept Arkansas law.