You can tweak the following query to help you determine if your user is a member of role/group 'module_dml'.
Then you can use it in a trigger function that does the logging.
SELECT g.rolname as group,
u.rolname as user,
r.admin_option as admin,
g.rolsuper as g_super,
u.rolsuper as u_super
FROM pg_auth_members r
JOIN pg_authid g ON (r.roleid = g.oid)
JOIN pg_authid u ON (r.member = u.oid)
WHERE u.rolname = '{your_user}'
AND g.rolname = 'module_dm;'
ORDER BY 1, 2;