Regardless, you cannot let your wife go in and stay outside. You can take someone in as a guest with you, not send someone in instead of you

The lounge access guidelines do state

If you are travelling with more than two children, the Qantas lounge manager will try to accommodate them, subject to reviewing the space available in the lounge

If you are unable to access the 1st class lounge, you may be able to access the business class lounge. Failing that, unless you have an AMEX card that provides for access to the AMEX lounge, I think you will just have to settle for not using a lounge if you all wish to stay together