PostgreSQL TRIGGER on WITH (UPDATE ..)UPDATE on 2 tables

Question

I have an SQL query like this:

    WITH whatever1 AS (
        UPDATE
            table1
        SET
            field1 = <some number>
        WHERE
            id = <id>
        RETURNING id, field1
    )
    UPDATE
        table2
    SET
        field2 = (whatever1.field1 * 100000000::BIGINT)::BIGINT
    FROM
        whatever1
    WHERE
        field3 = whatever1.id
    RETURNING
        field3 AS whatever2

and I have this trigger that does not let me do the UPDATE above:

CREATE FUNCTION public.function1()
RETURNS TRIGGER LANGUAGE plpgsql AS
$function$
BEGIN

    IF NEW.field1 != OLD.field1 THEN

        IF (NEW.field1 * 100000000::BIGINT)::BIGINT != (SELECT "field2" FROM table2 WHERE NEW.id = field3) THEN
            RAISE EXCEPTION 'Help me with this trigger so this exception is not raised.';
        END IF;

    END IF;

    RETURN NEW;
END;
$function$;

CREATE TRIGGER trigger1 BEFORE
    INSERT OR UPDATE ON public.table1
    FOR EACH ROW EXECUTE PROCEDURE function1();

Note the comparison part should be ok, because select 428872 = (0.00428872 * 100000000::BIGINT)::BIGINT returns true.

I guess the problem is with the chained UPDATEs not updating both tables at once. Replacing BEFORE with AFTER helps, but I don't understand all implications...

I actually read about CONSTRAINT TRIGGER, DEFERRABLE, INITIALLY DEFERRED and REFERENCING and I still understand nothing, but most if not all of them use AFTER TRIGGER, not BEFORE, it's even hard to test all possible combinations.

How to update the trigger so the top-most SQL query passes?