Sorry newbie, but growing fears about another fork in November. I guess similar question to the Bitcoin Cash ordeal which I missed.
Would your private key exist on both chains?
How do you know if you have a wallet that will support both coins in case you wanted to cash out? (For example something like Coinbase.)
How would you access and trade the resulting 'alt' coins?
Just treat them the same as any other new coin. Say that Bitcoin forks and becomes BTC2, there are obviously differences, if you would buy that coin with the changes, then keep your coins, otherwise, sell.