I'll kick the sacred cow too: I am driving a car that we bought new eight years ago, and it was absolutely the right choice.
At the point we bought, the price difference between a new and late-model-used Civic was less than $1000 (it may've been an unusual moment in time, but it was true when I bought my car). For that relatively small amount, we got exactly the car we wanted, and we knew it had no maintenance problems. It was just under 20K, and we paid cash. In eight years we've replaced the oil and tires, and we've purchased a lifetime alignment -- and that's it. I treat this car like a baby, and I really think we'll get 20 years out of it -- not bad considering the number of weekend trips we take.
However, I think you should go a little larger than a Fit. You say you can fit in three carseats -- good -- but you need to think long term with this purchase because NOT trading up is a good long-term strategy. My two girls are now adults, and they fit comfortably in the back seat of my Civic. Let one of them bring a friend, and they're cramped ... and I'm talking about a car one notch up in size. Three in the back of a Civic every day would be uncomfortable, and taking a weekend trip with five people in the car would be limiting in terms of trunk space. If you choose well, your three small children will be teens /adults, and you'll still be driving this same car. So consider your purchase with three teens /adults instead of three small children.
Now, about the money. If you're driving only 4,000 miles per year, you're not really losing that much money at the pump and the mechanics. Ask yourself honestly, are you just irritated with your current car at this moment, or do you have new car fever? Do you have to have it RIGHT NOW? Instead of reducing your investments, can you save aggressively for the rest of 2015 ... with an eye towards buying a 2015 when the 2016s come out?