Had several questions on the same matter, concerning my daughters and my sister and her wanting there socials. ?
1 attorney answer
Your sister is demanding money before she lets your daughters come home to you? That's called kidnapping. Call the police.
The EBT application is between your sister and the government. It sounds like fraud to me, but you should just ignore it.
If she claims your daughters as dependents, and you also claim your daughters as dependents, then both your tax returns will get held up, and you will both need to write letters of explanation to the IRS. I assume the IRS will eventually rule in your favor, based on what you have said here. But it's going to be annoying. Two and a half months does not make them her dependents.
With all that said, if she took in your kids for 2-3 months, it would be nice and reasonable for you to offer to pay some of the expenses. I assume your daughters ate food, took showers, used electricity, and incurred other expenses while they were there. Maybe you can offer something as a compromise and make this all go away.
Be aware that this response does not create an attorney/client relationship. I live and work in Massachusetts and may or may not know the local laws where you live. I hope people find my responses not only helpful but somewhat entertaining as well. If you rely on this as legal advice, remember the old saying, "You get what you pay for."