Both parties have children of their own and property and IRAs of their own with named beneficiaries-which are the children of the owner of the IRAs. Niether party has a will
Anything with named beneficiaries will go to that beneficiary. Anything that doesn't have that named beneficiary will go according to the intestacy laws in the state (for people without wills). It's a lot easier if these people decide to get a will, because then they can control where their property/IRAs/etc go.