Corrected passage
Once upon a time there was a poor miller who had three sons. When the miller died, the eldest son received his father's mill, the second son received his donkey, and the youngest son received only a cat. The youngest son was very unhappy.
Puss set off without delay to catch some rabbits. He caught two fine rabbits and took them to the king's palace. The amazed guards let the marvelous cat in boots, who was carrying a bag, into the palace.
'Your Majesty,' said Puss as he bowed. 'My master is the Marquis of Carabas. He sends you these gifts.'
What I changed and why (simple steps)
- Changed 'When he died' to 'When the miller died' so it is clear who died.
- Changed 'the eldest got his father’s mill, the second - his donkey' to 'the eldest son received his father's mill, the second son received his donkey' to be clearer and use consistent words.
- Changed 'got nothing but the cat' to 'received only a cat' because 'only' is easier to understand than 'nothing but'.
- Changed 'The poor fellow was very unhappy' to 'The youngest son was very unhappy' so we know who is unhappy.
- Moved 'without delay' to 'Puss set off without delay' — that sounds smoother in English.
- Changed 'could not but let' to 'let ... into the palace' so the meaning is clearer: the guards let the cat enter the palace.
- Made the speech punctuation clearer: started the quoted sentence with a capital letter and split into two short sentences for easier reading.
If you want, I can read this aloud, make it even simpler, or help you practice the changes together.