My child holds only a foreign passport — can I simply travel without telling the other parent?

No. The passport the child holds is irrelevant to the legal requirement. Israeli law governs children habitually resident in Israel regardless of their travel document. Leaving with a foreign-passport child without the other parent's consent is still treated as unlawful removal under the Legal Capacity and Guardianship Law, 1962, and as child abduction under the Hague Convention if the destination country is a signatory.