an alien child who—

(A) resides in the same household as a parent who has been battered or subjected to extreme cruelty in the United States by that parent’s spouse or by a member of the spouse’s family residing in the same household as the parent and the spouse consented or acquiesced to such battery or cruelty, but only if (in the opinion of the agency providing such benefits) there is a substantial connection between such battery or cruelty and the need for the benefits to be provided; and

(B) who meets the requirement of subparagraph (B) of paragraph (1); or