TornTools appears to handle this by diffing the total vault against the player's personal log for vault deposits/withdrawals. I suspect that if there was an easier process, TornTools would probably be using it.
I don't believe there's any way to use your own API key to query another player's logs. However, if a tool was using both your key and your spouse's key, it would know both of your deposits and withdrawals.
Property Vault History