I have three very lovely, yet very loud Chinese children living next door to me in my condominium. Two of the children are quite young, and I do realize children by their very nature are loud; without exception -- and at all hours -- they leave their apartment with their mother and are screaming. This can be loud, happy singing, or it can be frustrated crying. I am disabled and sleep quite a bit, mostly due to severe pain. The parents' English is not good; they are new here. How can I very politely (in writing) ask the parents that they please try to keep their children quiet in our common spaces, like hallways? They are very loud and noise travels far in our building. Thank you!
"希望您能多照顾一下您的孩子，他们经常吵闹，影响我们生活和休息。" (Please take good care of your kids, because they are so noisy and badly influenced our lives.)
Try not use "大叫" on your note, because that sounds like a bad comment on their kids, which may make them unhappy. Better use "我们" to show that you are a "general neighbor" like the others, instead of someone who cannot fall asleep due to your own reason (medical/phycological maybe, who knows). This politely tells them it is their fault, not yours.
Also, having both Chinese and English would also help, as is suggested in the comments you got.
Not sure how much politeness you're looking for, here's my input:
不好意思(mr. / mrs. X), 我最近有睡觉睡得不太好, 如果孩子们晚上可以安静一点, 对我来说这是一个很大的帮忙, 谢谢
"Excuse me Mr./ Mrs.X, I have trouble sleeping lately, if the kids can be more quiet at night, it will be helpful, thanks."
I did not mention about the common space thing as it might give them a false message that their kids can be as loud as they can in their house, but you can edit it to see fit. Also if they're not very nice people or if you want to be more forceful, Bfrguci's answer is a better choice.