May Allah (swt) bless his soul and raise him with Muhammad and his Ahlulbait (a.s).
It is recorded in Fiqhi books like Urwatul Wuthqa that if one is buried without Ghusl, it is obligatory that he/she must be exhumed and the Ghusl is performed on their bodies and then get buried again GIVEN that 1) the corpse is not decayed and 2) the act of exhumation is possible and also 3) the fact that the whole process is not considered a disrespectful act to the buried person.
There's no need for a wood chamber if you mean a coffin by that.
If the circumstances above are not possible at all then do not worry, Allah (swt) judges us according to our actions and let's hope that your father's actions be sufficient for getting Allah's Mercy. And you as his children can give charity and recite Quran and do Mustahab acts and gift the reward to his soul and it is very much recommended as the duty of children towards their parents!
These rituals are the duties of the alive people around the dead!!!