I'm going to take a different approach here.
Let your wife stay home. The amount she will probably bring in, won't probably make much difference, when you consider, you will both be tired, and the chances are the costs of working will wipe out many savings (unless she is able to get a full time job paying more than minimum wage)
There are transportation costs, clothing, and usually more money is wasted on take-out and groceries, because you are both tired.
Have your wife's job, be to reduce costs in the home as much as possible.
Reduce, reuse, recycle.
Line dry clothes etc.
Get rid of the second car asap. You only need one car.
Find ways to reduce cost.
Find ways to earn extra income at home...such as pet sitting in your home while people go on vacation?
Not just dogs, but maybe others such as hamsters, gerbils, rabbits, birds....the pets that boarding places may charge too much for th average family.
Does your wife have any talents...make delicious cakes, preserves, cookies...she could sell to your co-workers (you could take in samples , and maybe brochure of items/prices) , or maybe sell at a week end market?
Call the credit card companies and tell them you are having difficulties, and you want the interest rate reduced.
alternately
find new credit cards where you can balance transfers for 0% or low rates.