How to export some rows of multiple tables linked between them according to one column value?
you can, if you use a correlated subquery. Check the manual.

QUERY=son:"where exists (
    select * 
    from mother 
    where
        mother.id_mother = ku$.id_mother and 
        mother.last_updated &gt; trunc(sysdate,'month')"


ku$represents the table you are actually exporting, so here it is the table son.

Starting with Oracle 12c you have the VIEWS_AS_TABLES parameter. Then you can export  the data of a view and store it in a table, e.g. with sqlplus do

create view new_son
as
select son.*
from son, mother
where
    mother.id_mother = son-id_mother and 
    mother.last_updated &gt; trunc(sysdate,'month')"


Now export this using

VIEWS_AS_TABLES='new_son'


If you import this it will create a table new_son.