I know it looks like there's a lot of red but it's mostly just my commentary. You write very well!

An accident (there were two accidents)

Last Saturday, I went to a Chinese restaurant to attend a party. When we ("we" is plural - who else was with you? Perhaps revise the "I"  in the first sentence to "my family") were chatting with some new friends, my elder son fell down from the chair ("fell off the chair"比較口語化） and broke his chin (你的意思是他打破了下巴嗎？如果他沒有骨折，我們不用"broke"來形容. 比如說, "he broke his arm" = 他摔斷了胳膊. 你可以說，"hurt/injured his chin"）. One of my friends put some ice on his chin immediately so that the wound would not swell up. Therefore (你的意思是“因為他受傷，我們不吃了因為我們得趕去醫院”。在這裡，“Therefore"讀得不順。"Therefore" should refer to a reason that immediately precedes it, so you want the word to refer to his injury and not to the action that your friend took.) we couldn't continue eating because we should (had to) go to hospital.
In the hospital, we met a Chinese doctor. He was very kind. He put some glue on the wound and then put a plaster (bandage or band-aid) with a cartoon zebra on it. He told us that my son should wash his mouth with salt water after eating meal and he could take off the plaster (bandage or band-aid; or say "he could take it off") after 3 days. When we came back , it was 10pm. It was very late for the children (在這作文前面我覺得你可以介紹你有多少個孩子）because they usually sleep at 8pm. However, he （這個代名詞指的是一個人。如果你想說的是兩個孩子，應該用“they"） haven't ate (hadn't eaten) anything this (that) evening.So he (they) ate some food and went to sleep. He ("My elder son" - optional, but it's nice to clarify since you have two sons) looked tired and depressed. I consoled him, saying that he would be better the next morning.
The next morning, I asked him why he fell down from the chair (fell off his chair). I guessed maybe (I guessed he may have) put his feet on the table for fun because he is a playful boy. But (However,) he said he never do ("didn't do" - "never" 指說他一輩子都不會做出這樣的姿勢） that. I believed him and asked him to be more careful.
Last month, my younger son also broke his chin in the kindergarten. His teacher brought us (老師帶了你和你的兒子嗎？還是他只帶了你的兒子？Using "us" here is abrupt, because you were not mentioned in the previous sentence） to the nearest surgery clinic. The doctor also treated the wound like this (the previous doctor).
All in all, although it is difficult to avoid the accidents, I still hope that my sons can grow up safe and healthy. and I will be more careful to take (in taking) care of them in the future.