Here's the main problem with your story:
Your account was "hacked" by your brother and bets were made. In that event, is it not easy to simply claim that your account was used improperly and try to get a refund if you lost? You did not show the full log so it is unclear whether the bets actually resulted in wins or not (though it seems like it may have been implied)
Seems like your brother's 'prank' was also pretty stupid. If it went from 90 mBTC to 0 and back, that means all of the balance was placed on a bet that had a 1 in 15 chance to lose. If you share the account, why in the world would he decide to 'prank' you by potentially losing all of the balance? You use this account together but allow someone reckless to have the possibility of squandering your money?
Along with this, if you made $700, that means that the balance was multiplied by 9.32, which at the very least would take a spin on green @ $50. Your brother would do that? As you said, "his prank was to change the password and try to withdraw the money to another address," but did that actually include betting?