Man, I don’t want to go full Dave Ramsey but is going on here?
Make some lifestyle adjustments, reduce your spending, and free up cash flow to pay down credit card debt. Otherwise you’ll be in this situation again in the future.
Options in the shorter term: Look for a new credit card that has a limited time low interest period if you roll over your balance
No Intro Interest Credit Cards
HELOC and 401(k) loans as discussed above. Stop contributing to your 401k plans (beyond the company match) until the CC is paid off.
I couldn’t tell from your initial post but based on your wives desire to pay down the house are you guys making extra payments to the house every month? If so, stop that immediately and put that towards credit cards.
If you drive expensive cars, I’d sell them. Drive a low cost, paid off car.
Expensive gifts or vacation on the horizon? Cancelled until the CC is paid off.