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孩子们 (háizǐmen) refers to a plural of children. I don't recall ever reading parents referring to their children as 孩子们.
Question: Can 孩子们 belong to the same family?
I'm not sure how to answer this myself. Searching for, e.g. “父母的孩子们” gives e.g.
那些有着强势父母的孩子们,后来都怎么样了?[src]
which don't belong to the same family.
Quote:- "...I don't recall ever reading parents referring to their children as 孩子们"
That's because under normal circumstances it is too formal to refer to or address your children as such. If you say or address your children as 孩子们, the 们, (which in Chinese could in some context connotes a certain formal societal status or ranking), would be like calling or addressing your children as "my progeny", unless of course the special circumstances or context calls for it. (for example in drafting a will)
So, in the Chinese context you could use 孩子们 when, for example making a formal speech or about to give some sagely, fatherly advice, like,
孩子们, 我有个好消息。你们大哥，聪明, 毕业为医生. 希望他的成就会鼓励我们家的孩子们努力读书。
"My children, I have good news. Your elder brother, 聪明, graduated as a doctor. Hope his achievements will encourage our family's children to study hard"
(Well, assuming this guy has 3 wives and 15 kids)
Sure.
You can look up a phrasing like 我们家(的)孩子们 and you will quite a few results. Here are some snippets of titles and phrases for example:
孩子 can be both plural and singular without 们, depending on the context. You'd be more likely to find a combination of 我们家 and 孩子 to encompass all the kids in the family without especially stating "们."
It can belong to the same family and different families depend on the meaning you want to express and context.
As the example you give, 那些有着强势父母的孩子们,后来都怎么样了? 那些有着强势父母的 determine the characteristic of the 孩子们 (children). All the children confirm this condition (那些有着强势父母的 Have strong and exalted parent) are the kind of children mentioned in your example. No matter they come from the same family or not.
However in this example, that kind of children have more probable from different family with different parent, since there are a lot of people can fall in this category.
