Is it permissible for my parents to be considered as my maternal cousin's own parents, given that she is my milk sister and is living with us as a family member due to her mother's passing?
Milk daughter is not allowed to marry with her milk father nor her milk brother, but she does not have a share in inheritance like a real daughter unless by a will and within the limit of the one third. As she is living with your family due to her mothers passing away, you and all your family members should give her all moral support and look after her in every possible way.
Wassalam.