SELECT name, 
plastname,                                       
strftime('%Y', 'now', 'localtime') - strftime('%Y', birthdate) as AGE,
department.section,
emp.id as id
FROM emp Inner Join department ON emp.id_department=department.id
WHERE strftime('%d-%m', birthdate) = strftime('%d-%m', 'now', 'localtime') 
UNION
SELECT fistname, 
lastname,                                        
strftime('%Y', 'now', 'localtime') - strftime('%Y', birthdate) as AGE,
'Wife of '  || (SELECT name || '  ' || plastname FROM emp e WHERE e.id=wife.id_emp),
id_emp as id
FROM wife
WHERE strftime('%d-%m', birthdate) = strftime('%d-%m', 'now', 'localtime')

P.S.  add fix

You initially chose to store birthday data in three different tables, at least in this example.
These tables do not have any links with each other.
'Emp' works, while the wives and children go out on their own and in different places.

The final table in the form you point to displays data from THREE TABLES using a query
that combines the data for output using a UNION.
Unfortunately, in this case, it is problematic to display information about the ID and belonging
to the table.
Therefore, an error message is displayed that indicates that it is impossible to determine a unique identifier.
Solution:
Wrong - Sculpt various patches, where something is constantly wrong and not molded.
Correct - Recreate the database, taking into account the relationship between the employee and relatives)))) (Wives, children, etc.).
There should be strict relations in the family and not whoever wants where)))). And the program will get easier.

Derek's solution is just a temporary fix until the ID matches or is missing.