1) When you buy something at a store like Target, WalMart or a grocer, you can usually get an option for getting cash back (if you are using a debit card). You must know your PIN.
2) Go by the bank. Withdraw cash directly from the bank or ATM
3) If you take care of the credit card, you can find a provider that takes Visa/Mastercard. If you don't want your transaction to be tracked, buy a gift card at the grocery store for the amount you'll need.
4) Get in the habit of paying for some things with cash. Gas, restaurants, etc. It's less suspicious if you're carrying around cash, that way. Also, make sure your wallet has hiding places. Tuck away $5, $10, $20 every time you get a chance.
All of this is much easier if you handle the family finances and taxes.
Sometimes you can get direct deposit into two separate accounts by percentage, check with your HR department.
You can tell HR it is a savings account
You can tell the spouse it's just a retirement fund (if they can see the split at all - they would need to see the stub and that's not always sent with a direct deposit)
Most likely you can just siphon off a bit into a separate play account, it might take a bit to build up, but once it does, it'll be stealthy.