Yes, listwallettransactions only shows transactions which are directly relevant to that node's wallet. A transaction between node 1 and 2 isn't relevant to the wallet on node 3.
Assuming you don't want to do this for too many addresses, your best bet is to use importaddress to add the relevant addresses to node 3, as watch-only addresses. You can then view those transactions in listwallettransactions if you set the third parameter includeWatchOnly to true.
Another option is to query the blockchain in general using the getblock call, passing true in the second parameter format. The output will include a list of tx IDs in the block, and you can then retrieve individual transactions using getrawtransaction with the second parameter verbose set to 1.
Your final option is to use the MultiChain Explorer (in development), though that's more involved.