You're wrong. You have the longer blockchain which doesn't contain the transaction to the exchange. Your blockchain gets accepted by the network.
How exactly will you have a longer blockchain if you rewrite your synced blockchain with an older one?The older one will not contain the transaction to the exchange, true, but once it updates and syncs, your client will see you already spent your coins.
What exactly are you trying to prove here?
Dude trust me, if it was that easy, crypto would not exist anymore.