"Los niños están bien, gracias."
Translation:The boys are well, thank you.
"estar" is for states/moods or places/positions. I'm here - estoy aque, estoy triste - I'm sad. estamos con él - we are with him... "Ser" is used when you need to give information about someone or something, to describe... Soy malo/Soy mala - I'm bad/mean/evil, Es verde - It's green... I'm Carlos - Soy carlos. I'm a fool, soy un tonto... If you say "Los niños son bien" I would personally understand that they are nice, cool, gentle. but if you say "Los niños estan bien" you are telling someone they are ok, healthy, safe
Since estar is 'temporary' why would 'the kids are doing well, thanks' not be correct? They're doing well now, maybe not once I get el cinturón (kidding).