I think "Is that my child?" would be "Je to moje dítě?" Just as in English, there are two sentences with slightly different word order, although their meanings are about the same.
This has been discussed thoroughly for other sentences before and the large consensus within the team is that the difference is significant.
My personal understanding of those two Czech syntactic variants is that they are very different for most sentences. On the English side I let it to others.
'it is my child?' Reported. I am going for plural english locutions. Your subtlety is lost on me since the notes say my and mine are the same. After all, Czech has its freedom with word order too. (Such tea-cup storms have gone on often in other Duo languages.)
The order is quite free, but not arbitrary. This change does change the syntactical structure.
You can see the difference with Je to můj stůl? vs. Je ten stůl můj? You cannot just shuffl the words to Je to stůl můj?, that is impossible. It is NOT just a word order issue.