La. Civ. Code art. 258
If the parents are divorced or judicially separated, only the one to whom the court has entrusted the care and custody of the children has a right to appoint a tutor for them as provided in Article 257. However, if the parents have been awarded joint custody of the children, then the right to appoint a tutor for them belongs to the parent dying last, but either parent may appoint a tutor of the property of the children as provided in Article 257. In the event that both parents appoint a tutor of the property of the children, the tutors shall separately administer that portion of the children's property which is attributable to the respective parent's estate. The court shall decide which tutor shall administer that portion of the children's property which is not attributable to either parent's estate.
La. C.C. § 258