What are the rights of children over their parents, and are children to be blamed if parents fall short in fulfilling these rights?

If a father falls short in fulfilling his children's rights, the blame is on him. However, this does not negate the children's duty of filial piety towards him. Honoring parents is obligatory, even if they are disbelievers, as Allah Almighty says: "But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them, but accompany them in [this] world with appropriate kindness."