The pasuk says "banim atem lashem elokeichem," referring to us. Is there a drasha anywhere (or another source) that says that non-Jews are not called Hashem's children? (I don't think this would really make it an issue to tell non-Jews that "we are all God's children," as we would be using the words colloquially and not in a halachic sense, but curious nonetheless).
If you do not object to interpreting a prophet yourself, I would consider the words of Amos 9:7:
הֲל֣וֹא כִבְנֵי֩ כֻשִׁיִּ֨ים אַתֶּ֥ם לִ֛י בְּנֵ֥י יִשְׂרָאֵ֖ל נְאֻם־יְהֹוָ֑ה הֲל֣וֹא אֶת־יִשְׂרָאֵ֗ל הֶעֱלֵ֙יתִי֙ מֵאֶ֣רֶץ מִצְרַ֔יִם וּפְלִשְׁתִּיִּ֥ים מִכַּפְתּ֖וֹר וַאֲרָ֥ם מִקִּֽיר׃
To Me, O Israelites, you are just like the Cushites—declares the LORD.
True, I brought Israel up from the land of Egypt, but also the Philistines from Caphtor and the Arameans from Kir.