SELECT Family_Id FROM tblFamilies WHERE Family_Name = TT_Child_Last_Name

ALTER PROCEDURE [dbo].[usp_Z_Insert_Children]
@my_TT_Children TT_Children READONLY
AS
BEGIN
    INSERT INTO tblChildren(Child_FirstName,
                            Child_LastName,
                            Child_Family_ID)
        SELECT Cld.tt_child_FirstName,
               Cld.tt_child_LastNAme,
               Fml.Family_Id FROM @my_TT_Children Cld
                    INNER JOIN tblFamilies fml
                        ON Cld.TT_Child_LastName = Fml.Family_Name
END

INSERT INTO tblChildren(Child_FirstName, Child_LastName, Child_Family_ID)
SELECT Cld.tt_child_FirstName,
Cld.tt_child_LastNAme,
Fml.FamilyID
FROM @my_TT_Children Cld
INNER JOIN tblFamilies fml on Cld.TT_Child_LastName = Fml.FamilyName