If you received BTC from your dad or brother who also purchased BTC from coinbase then they may think that you are in control of their accounts and this may be behind the question of asking about other coinbase accounts that you have. If this was their thought process, then they might be afraid that you were using multiple accounts to get around their daily limits, which could potentially expose them to additional credit risk.......this is of course speculation.
Yeah that makes sense but honestly we are not talking about thousands of coins or anything like that, we are talking low small fry numbers. If they truly yanked by account for 10 or 20 coin transactions here and there I would be very surprised. Looks like their policy over there is
guilty unless proven innocent, or rather
guilty guilty guilty despite evidence proving innocence. I'm gonna use Bitstamp from now on
I was/am obviously speculating, however if you were to have only one small tx linked to your dad's and brother's account and each of those accounts has a daily limit of buying $10,000 per day then they would be exposed to $30,000 worth of exposure per day if you were to attempt to do something malicious with all three accounts.
I am not trying to defend their actions, but rather try to determine some kind of explanation as to why they might have closed your account.