Because "ty ženy" is stressed, it is the new information that the sentence brings. It is them who take care of her.
Ty ženy staraji se o ni. is acceptd. The meaning is different though. We stress o ni. It is her of whom the women take care. She is the new information brought by the sentence.
I find the word order very difficult like that. To me it would be much more natural would as it were: "Ty ženy se starají o ni." Would that be correct too and which word order would a Czech person use?
U nás je to slyšet správně. S tím, že nejde spustit zvuk, se můžete obrátit na samotné Duolingo, ale asi o tom už vědí. Tak mne to rozčiluje. Včera nefungovaly odkazy do dizkuzí, dneska už diskuze neotevřu na Firefoxu vůbec.