Translation:How old is your child?
I don't know, but I'm guessing you'd use a pluralizing suffix: 達 (たち) or 等 (ら).
I'm still learning, but I found this resource useful:
I think it is not a good manner to use posessive phrases excessively in Japan as long as it is understood. In case a specification is necessary, it will not always be あなたの，and there are other choices of expression. e.g. calling the parent by family name (if you know) or そちら様 (if you don't know) would sometimes be necessary.
If you ask a question, it's more often implied that you're talking about something related to the listener, because if you're asking whether or not that is your child, you might be a bad parent. If you ask if that is someone else's child, you'd use their name. You come off a bit rude in Japan if you say "あなた," so try to ask their name or something before asking whose child is running around.
It's definitely something that's said in English, at least in America. I've heard it spoken by Eastern and midwestern Americans. Usually the intonation is a bit different... so for example it'd sound like "Your child is HOW old?" Indicating that there's a disbelief behind it. Not sure what the Japanese equivalent would be.