What is the correct relationship for a child, when the taxpayer has legal custody?

"am I reporting the relationship the correct way?"

There are legal relationships and even no relationships (just responsibility), such as: children, foster children, adopted children, and just having custody, as well as minor, or adult; and guardian.

For Tax Purposes, you are asking about Dependents.

None of that is equivalent. And what to use depends on what you are using it for.

Adopted Children are family. Foster Children are placements.

What's the harm in using daughter? Especially since the custodial adult thinks of them that way.

A foster child is any child placed with the taxpayer by an authorized placement agency or by judgment, decree, or other order of any court of competent jurisdiction.  It is not an adoption, and the placement or order can always be changed, but if she wants to tell the world that these are her daughters, she can as long as it's not for fraudulent purposes.  She should tell IRS that they are foster children, and make sure they qualify otherwise as dependents.  Suggest she go be sensitive about it elsewhere, you're busy now.