Let's just clarify something.
If "stepdaughter" means you had a legal marriage to the other parent, then your rights as a stepparent for tax purposes are lifelong and do not end even if the marriage ends. The child is still considered your stepdaughter for income tax purposes as you have the same rights to claim her as a dependent as a biological parent or grandparent. In this case, if the child lives in your home more than half the year, you can claim her and the grandparent can't.
On the other hand, if you are using the word "stepdaughter" for an informal relationship with a partner who you were not legally married to, then you are not the child's stepparent for tax purposes. The child can be your "other" dependent if they live in your home the entire year and earn less than $4300 of their own income. The grandparent still can't claim them even if you are not a legal stepparent, because the child did not live in the grandparent's home.
Lastly, even if you were never married to the other parent, if you were made a guardian by an action of the courts (guardianship, foster child, etc.) then you do have the same legal rights as a biological parent.
