I'm Doug, and I'm very sorry to hear of your family's situation. My goal is to provide you with excellent service today.
Quite simply, the only rational thing to do is for your husband to immediately file a formal criminal complaint with the police and accuse her of Extortion. The neither of you should have any further contact with her, whatsoever.
Continuing this charade---and especially giving her money of any amount---looks like a payoff for silence and opens up the suggestion that your husband is actually guilty of her ridiculous allegations.
Keep ALL present and future emails that you receive from your niece. She is poised to ruin your family based on her allegations, and your husband's past financial support of her is motivating her present behavior.
Regardless of whether she gets straight inn rehab or not---the best thing you and your husband can do---now and forever into the future---is cut off all ties to this very dangerous threat to you and your marriage.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
Please be so kind as to rate my service to you. That is the only way I am credited for assisting you.
I wish you and yours the best in 2016,