Quite a good little story. Just check your punctuation here and there - note, there should be a comma BEFORE the speech marks when someone has finished talking. Also check that the words you use to describe the beach are appropriate. You seem to have two stories in one here - the argument with your sister and the one about the beach. It might have been better to focus on the second one on its own.
Notes:
1. “Come down Michael were going, to go[,]” my mum
2. “Alright I’m coming “, I replied [should be: “Alright I’m coming," I replied
3. for I long argument [after a long argument]
4. she replied back [you don't need to say 'back' when you use 'replied']
5. precised [should be 'precise' but is this the best word anyway here?]