Can 孩子们 (háizǐmen) = "children (plural)" belong to the same family?
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:


看看我们家的孩子们
《家教之我们家的孩子们》
我们家的孩子们真棒!




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."