I take Cleve's $695, subtract the oil change and the gas to get $425, then add 44.5 cents/mile (the IRS allowance) for 2000 miles = $890 for fuel/wear&tear, and I get $1315.00. [The oil change isn't the only maintenance issue; there are the tires, the shocks, the filters and belts, etc. Also, if your vehicle is leased, 2K miles is a fairly large chunk of your allotted annual mileage.]
In addition, what kind of job does your DH have? What kind do you have? If either of you are paid on an hourly basis, don't forget to factor in lost wages for the extra day (or even two days) you will spend in travel time, presuming you are not willing to shorten the actual "fun" part of the vacation to compensate for the time you spend on the road. We're salaried, but we still like to look at the value of the extra vacation time used, in our case, it comes to several hundred dollars for one extra day.
Whether or not the AAA mileage calculator is reliable, gas is the least of it. Calculating the costs on "gasoline only" badly oversimplifies the true cost. Depending on your circumstances driving may still be less expensive than flying, but you should take all costs into consideration for the comparison.