As your tables are not large, try using a sub-query:
SELECT parent.id_parent, parent.name,
COUNT(pos.id_pos) AS q,
(SELECT COUNT(*) FROM children_detail cd WHERE cd.id_child = children.id_child) as cdc
FROM parent
LEFT JOIN children ON children.id_parent = parent.id_parent
GROUP BY parent.id_parent ORDER BY parent.name
Edit
Sorry, the following one should also work:
SELECT parent.id_parent, parent.name,
COUNT(pos.id_pos) AS q,
COUNT(cdc.id_detail) as cdc
FROM parent
LEFT JOIN children ON children.id_parent = parent.id_parent
LEFT JOIN children_detail cdc on cdc.id_child = children.id_child
GROUP BY parent.id_parent, parent.name
ORDER BY parent.name
Edit 2
If all else fails, you can use two sub-queries (very bad practice but should be fine for tables of your size):
SELECT parent.id_parent, parent.name,
COUNT(pos.id_pos) AS q,
(SELECT COUNT(*) FROM children_detail cd WHERE cd.id_child IN (SELECT cc.id_child FROM children cc where cc.id_parent = c.id_parent)) as cdc
FROM parent
LEFT JOIN children c ON c.id_parent = parent.id_parent
GROUP BY parent.id_parent
ORDER BY parent.name