A: Arkansas is not a community property state, but that doesn't change the answer to your question. If her name is not on the car note, she cannot be held responsible for that debt unless the divorce judge makes her responsible. Even in that case, the only person the financing company can come after is the husband. In that case, he might take her to court for contempt for not paying for the car.
A: If the mother of the child does not agree to the name change, you will have to petition a court to change the birth certificate. There are several factors that a court will use to determine whether it is in the child's best interest to allow the name change.