Yes, you are correct about the order. Pay off the smallest balance first, then incorporate what you were paying towards it into the monthly payments for the next debt on your list. In your case, Credit Card #2. When that is paid, add all of what you were paying towards it (credit card #1 AND credit card #2) towards the next item (the car). You continue to pay the minimum on everything except the smallest debt. Obviously, once the smallest debt is gone, the next one on the list becomes the smallest, and you pay extra until it is gone and move on down the list.
If you could get something to drive (a beater car) and be debt free on the car for $5,000 ($3-4,000 to get un-upside down, plus a grand for a beater car bought with cash) and your other debts totaled, say $8,000 (instead of the $1850) then I think you would get out from under the car first, and then use your "car payment" money to pay down the other debts (credit cards). But since it will cost you more cash up front to get out from under the car payment (minimum of $4,500 probably?), than it will to pay off the credit cards, I think you should get the credit cards paid off first. Then apply those monies towards the car until you get it down to something where you can sell it and buy something with cash.
(If you can get $7,000 for it, and get your loan balance on it down to $5,000... then sell it. And take the $2,000 you make on the sale to go buy a beater for CASH. NO LOAN). Then you will have income freed up (cash) every month to save for whatever your priority is. Whether it is more emergency fund (the 6 months variety, not baby step one of $1,000), a better car that you pay cash for up front, extra payments on the house to pay the mortgage off early, or to invest. His whole theory/plan is designed so that you have no PAYMENTS. To have payments, you have to have DEBT. And then you have no cash... it's all "spoken for" already when you get your paycheck each month.
Since your credit card debts are so small compared to the upside downness (?) of your car, then you should get the credit cards out of the way first. You'll just have to suffer through for a few more months (stupid tax is what Dave usually calls it, lol) until you get where you can act regarding the car.