It's not a good idea to do this with a non-deterministic wallet. Each time you send bitcoins, bitcoin-qt generates new private keys to add to the key pool. These are entirely random. Eventually the two wallet copies will diverge and you'll have different private keys in them. It'll be very confusing and you risk loosing bitcoins.

If you want to share a wallet on different computers use either a web wallet or a deterministic one like electrum.