The father needs to file for custody. It would help to provide a more complete answer if you explained what the current custody situation is. Does he have parenting time? Is it joint custody? Does the mother have full custody right now?
In any case, your fiance needs to petition the court for custody of the girls. If he has good reason to believe that the mother is putting them into danger, he can file for temporary emergency custody based on immediate danger.
Also, you might want to consider requesting that the court appoint a custody evaluator to determine who it would be best for the girls to live with (this will have a significant cost).
I would advise that your fiance hire a competent family law attorney to handle all of this.
My responses to posts on AVVO are not legal advice, nor do they create an attorney-client relationship. In order to provide true (and reliable) legal advice, an attorney must be able to ask questions of the person seeking legal advice and to thus gather the appropriate information. In order for an attorney-client relationship to exist, you and I both have to agree the the terms of such an agreement.
Sign up to receive a 3-part series of useful information and advice about child custody law.