Does anything remain binding upon my sister after her death, given that she vowed to slaughter an animal during an outing upon the birth of a child to her brother, and my husband fulfilled this vow?

The conditional vow is disliked. If the condition is met and your sister vowed something permissible, she is not obligated to fulfill it, and therefore, nothing is incumbent upon her. As for your husband fulfilling the vow on her behalf, it is not valid unless he willingly donates the money to her and she gives her permission; otherwise, it is not valid, due to the requirement of intention in expiation.