Three sets of rules decide where money goes, and they run in a fixed order. First, contract: a retirement account, a life insurance policy, a transfer-on-death account and an annuity pass to whoever is named on the form, and the will has no effect on them. Second, title: property held in joint tenancy with right of survivorship or as tenants by the entirety passes to the surviving owner by operation of law, again without reference to the will. Only what is left after those two reaches the will, or, if there is no will, the state's intestacy statute. In a blended family the first two categories are where the surprises happen, because a beneficiary form signed during a first marriage keeps working exactly as written until someone changes it.
The mutual will is the second failure, and it looks like a plan. A couple who each leave everything to the other, with the children named to inherit afterwards, have not created any obligation on the survivor. Once the first spouse dies, the survivor owns the property outright and is free to write a new will, remarry, or spend it. The first spouse's children have no claim, and nothing has gone wrong legally; the arrangement simply never contained the promise the couple thought they were making. This is the specific gap that marital and bypass trusts, and the qualified terminable interest property election in particular, were built to close: they let the survivor have the income and the use of the property for life while fixing who takes what remains. The instruments themselves are a subject of their own and are covered on their own pages.
The stepchild's default position, stated as precisely as it can honestly be stated. A stepchild who was never legally adopted is generally not a descendant under a state's intestacy statute, so if a stepparent dies without a will the stepchild ordinarily takes nothing while the stepparent's own blood relatives take. But "stepchildren inherit nothing" is too strong as a national statement, and the exceptions are not curiosities. Ohio's statute reaches stepchildren before the estate escheats: Ohio Rev. Code 2105.06 provides at (J) that "if there are no next of kin, to stepchildren or their lineal descendants, per stirpes," and at (K) that "if there are no stepchildren or their lineal descendants, escheat to the state." California takes a different route, recognizing a parent and child relationship with a stepparent for intestacy where "the relationship began during the person's minority and continued throughout the joint lifetimes" and where clear and convincing evidence shows the stepparent "would have adopted the person but for a legal barrier," under Probate Code section 6454. And the ground moves in both directions: South Carolina's intestacy statute carried a stepchild subsection until a 2013 amendment deleted it, which its own history note records. The reliable statement is therefore the narrow one. Adoption aside, a stepchild's position is fixed by one state's statute read on one particular date: the general default is that the stepchild takes nothing, and a state that does provide for stepchildren may do so only as a last resort before the estate escheats, as Ohio does, or by treating a qualifying stepchild as a child of the stepparent, as California does. Those are two different routes to two different results, which is why the question cannot be answered nationally.
Adoption is the bright line, and it cuts both ways. An adopted stepchild is a child for inheritance purposes, taking from and through the adopting stepparent like any other child, which is why adoption resolves the intestacy question that a lifetime of raising the child does not. Adoption generally also severs the legal relationship with the parent whose rights were terminated, so the child may stop being an heir of that side of the family. Both consequences follow from the same act, and neither is reversible by intention.
Remarriage creates rights the couple did not negotiate. Under federal law a new spouse becomes the default beneficiary of the death benefit in an employer plan such as a 401(k), and under state law a surviving spouse generally has a statutory claim on the estate that a will alone cannot defeat. A prenuptial agreement is the usual response and it cannot do the whole job, because a plan survivor benefit can only be waived by a spouse and a fiancé is not one yet. That mechanism is covered in full on the prenuptial agreement page.