Can an adult who has one deceased parent sue the other parent for part of the life insurance settlement?

If the other parent is the sole beneficiary in the life insurance policy, no. Participate in the probate process and you might walk away with something. So sad that someone's child would sue their grieving parent. Only if there is some record that the deceased parent wanted the child to have part of the money. If nothing...the insurance company gives the money to the person that has been chosen as the beneficiary. That is all they are required by law to do.