"They saw their child last weekend."
So in the examples where you don't NEED to use the 了, they're all prepositional phrases (but you can). "Yesterday he was in New York" 他昨天在纽约。In English, we may think automatically that this guy is no longer in New York. But if we use that sentence in Chinese, we don't know where he is. He may still be in New York, he may have moved to Beijing, we don't know; we only know that he was there yesterday.
That's important because: if you say 他昨天在纽约了 , we now know that he is done with New York. 了 is used as a "completion of action," so using it here isn't just like adding an "-ed" to the verb (as we usually can).
TL;DR 他昨天在纽约 = Yesterday he was in New York.
他昨天在纽约了 = Yesterday he was in New York (and now he's done with New York).
I think this is incorrect. It might be OK, but 孩子 generally is not assumed to be the 他们's if not specified. I think there should be a way to report the answer being wrong when you get it correct, since I wanted to but there was no way since there were only those few cards.
It should be 他们上个周末见了他们的孩子。
The sentence is still correct with the placing, but it should look out for incorrect syntax and add a few things to make it more clear.
Still, a pretty good translation.
This lesson is almost impossible to complete. The 2 forms of word for weekend are interchangeable used in answers, but without any clue, student must put the correct one in to get a correct answer, as it will only accept one. I copied your "correct answer" and pasted it the next time the sentence came up - still gave me an error: 他们上个周末见了孩子。Copied and pasted
他们上个周末见了孩子。wrong, here's correct answer.
I'm frustrated . . . this is a long way from the quality of the Spanish version!