If she is remarried, her spouse has the same rights to claim stepchildren as dependents as a biological parent has. If they file a joint return for his income, then she is "filing a return."
The parent who is automatically entitled to claim a child as a dependent is the parent where the child lives more than half the nights of the year, regardless of any court orders or divorce agreements. The non-custodial parent can't claim anything unless the custodial parent signs a release form. (In some cases, the non-custodial parent may be able to go to family court to get an order that the other parent sign the release, but the IRS won't do anything without it.)
