The reason why I'm asking is that some "Bitcoin banks" seem to only credit received coins after a given number of blocks have passed. If it would be possible to bind a transaction to a specific block chain (e.g., by specifying a required "previous" block) one could avoid this problem, by instantly crediting received coins, but by binding newly sent coins to the same fork of the chain where the previous coins have been received.
That wouldn't solve the problem. Even if you specify a required previous block, there is still no way to know whether the subsequent block that contains this transaction will "win" until sufficient blocks have passed.
In fact, this would make things worse. In the present system, if the block containing the transaction doesn't win, at least you can still perform the transaction if the sender hasn't maliciously attempted a double spend. With your scheme, if the block containing the transaction doesn't win, there is no chance to still perform the transaction.