Or just skip the whole Wallet1 and Wallet2 setup altogether... and simply go: Buy Bitcoins -> Send to Mixer -> Your Wallet

That way, the ONLY coins in a wallet/address of yours has come from a Mixer (plus you save on one transaction, not that that really matters much with today's fees )

Also, as others have mentioned, mixers help enhance your privacy, and will stop "most" people from being able to track your coins... but they probably shouldn't be considered 100% foolproof.