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If the husband is on the birth certificate as the father of the children, then he is presumed to be the legal father. As the legal father, both he and the mother have exactly equal custodial rights to the children. That means that whoever has physical custody of the children has the legal right to do so and the other parent can't compel them to turn over custody without a court order.
So the short answer is yes, he can legally take the children with him if he is on the birth certificate.