From what I understand, staking rewards are not automatically re-staked.
Is there some kind of option to automatically re-stake the rewards, or is there an easy way to make sure that all of my staking rewards are re-staked as soon as I earn them?
In order to restake the pending rewards, a payment transaction need to be sent from/to the affected account. ( for that purpose, sending a zero algos transaction from and to the same account would work just fine ).
On thing to remember, is that you need to balance the rate at which this transaction is sent with the gains you have and the transaction fee costs.
As far as I know, there is no automated mechanism on the Algorand block chain that would provide that, but maybe an exchange would implement this feature for you. Note that if you had two accounts, you could have moved 0 Algos between the two, and both would materialize the pending rewards.
The two-wallet idea makes sense, thanks.