Thanks for the responses everyone! I'm not going to take the time to respond to everyone, but know that I did read and consider all that was said!
First of all I'll just say my wife is awesome and I'm lucky to have her. We are definitely on the same page financially, which is great. We currently are a two car family, with the 2008 Cobalt and a 2011 Ford Fiesta [both have manual transmissions:)]. We have discussed cutting back to one car in the past, but without going into too much detail here, it doesn't appear that it would save us any significant money without making our lives significantly more complicated (including ideas such as moving closer to one of our jobs, which are both in areas with far less affordable housing than our current location nestled comfortably midway between the two). In addition, one car is essentially paid for by mileage reimbursements I get due to frequent work-related travel to other facilities.
As an aside...We actually (Gasp!!!) bought the Fiesta new (special factory ordered base model with zero options), and I do not regret that decision at all. It has turned out to be a very affordable car. I have been doing a bit of an experiment the last 3 years comparing the cost of ownership between our cars (including fuel, maintenance, repairs, insurance, fees, and depreciation) and so far the Fiesta has been surprisingly only slightly more than the Cobalt in terms of "normalized" cost-per-mile ($0.33/mile vs. $0.29/mile). That is, cost-per-mile adjusted to account for the fact that the Fiesta's cost per-mile is lower ($0.27/mile over 59,000 miles in 3.5 years) than the Cobalt's ($0.38/mile over 26,000 miles in 3 years) due to spreading the cost of annual expenses over more miles.
Although we plan to keep the Fiesta and it should work fine (not sure if the rear-facing seats will fit), I don't see the request to have a decent-sized family car at all unreasonable. We are big fans of doing cross-country camping road trips and also like to make frequent (read: monthly) weekend visits to our family who all live >200 miles away. That is a lot to ask of a Fiesta from a family of four. In the case that our family continues to grow in the future or we find a mid-size sedan to be insufficient, we would swap out the Fiesta for something like a minivan.
Anyway, as far as the car purchase cash vs. loan thingy...I hadn't thought about the effect on insurance premiums. That is an interesting point I hadn't considered, and that definitely swayed me towards cash until I thought of another none-of-the-above idea. My new plan, if/when I decide to buy, is to sign-up for a new rewards credit card, use the car to cover the spend for a juicy sign-up bonus, collect additional 1%ish points, and immediately pay off the balance in cash.
As far as the car decision itself, I've communicated a very low, firm offer to the dealer ($2000 less than the amount I mentioned before and $4000 below their asking price). They seemed to be quite offended with my offer, but maybe they'll call me back later. The comment about making up any "loss" on the trade-in with the cost of the newer car was absolutely correct, but I just look at things in terms of net transaction price. I figure if they accept my offer, the next 3-4 years worth of depreciation will be covered in the deal. Meanwhile, I will keep looking for other potentially more budget friendly options. I've got 6 months until the babies arrive, and there is no immediate rush after that to make the switch unless we can't fit them in the Fiesta.