Acho que a única coisa que o OP faz de errado é
join a chave errada. de qualquer forma tente isso primeiro.
SELECT t.id, t.feedback, t1.note as note, p1.name as parent1, p2.name as parent2,
p3.name as parent3
FROM tblChildOfChild t
LEFT JOIN tblChild t1 ON t.tblChild_key = t1.id
LEFT JOIN tblParent1 p1 ON t1.tblParent1_key = p1.id
LEFT JOIN tblParent2 p2 ON t1.tblParent2_key = p2.id
LEFT JOIN tblParent3 p3 ON t1.tblParent3_key = p3.id
WHERE t.id = 1
