Translation:He comes with his children and we with ours.
Are you sure this is correct English? It sounds wrong to me, and seems to be using an object pronoun ("us") as a subject pronoun ("we").
"nous" is the subject of the verb "vient" (come), which apparently doesn't need to be repeated in French (also true in English). Seems like using "us" would only make sense for something like "He comes with his children and us" (where the object is "his children and us").
Msinykin, In UK English "we" is the subject of a sentence and "us" is the object. So "we" needs an verb to make sense not a preposition, we sing, we dance, we drink, we enjoy etc. So "and WE COME with ours" is how this makes any sense to a UK English speaker and NOT "WE WITH ours". Horses for courses, so you maybe like the French English version but I don't. IT's a French learning course, so why am I being force fed bad English.
I agree that it is ellipses: in both French and English there is no need to repeat the verb ("venir" / "come"). So your sentence is perfect and matches Duo's preferred answer.
But the question in this thread is whether "He comes with his children and us with ours" should be accepted. That is, can "nous" be translated either as "we" (subject) or "us" (object) in this sentence. And although it is fairly common in English to use an object pronoun as a subject pronoun, it is not grammatically correct and so I don't expect Duo to accept it.
I think the verb is "vient" for both subjects "il" and "nous"; and just like in English it doesn't have to be repeated as "Il vient avec ses enfants et nous venons avec les nôtres." -> "He comes with his children and we come with ours."
As @piguy3 says, this is "ellipses": you can omit the second "come" so "we come with ours" elides to "we with ours".
The verb is "venir" / "come" is used intransitively (no object), and the objects of the two prepositions "avec" / "with" are "ses enfants" / "his children" and "les nôtres" / "ours".
Thank you for explaining that, Sitesurf. Like Darth, I was marked wrong for using "kids" -- but the explanation I was given for the error blamed the missing second "come". If I hadn't come here and seen your post I would have no idea that the fault lay in my use of the word "kids".
I disagree it shouldn't reappear in English.
The default translation "He comes with his children and we with ours" sounds pretty awkward. I'm not saying it's incorrect (I didn't check it) but it does sound odd and it shouldn't be the default from my point of view.
I think "He comes with his children and we come with ours" (which is accepted) should be the default.