I echo Steve's suggestions. If your are trying to save a few bucks, that would be the best way to go. I absolutely loathe paying for a parking spot ANYWHERE, but I always seem to fly alone, so my wife always drops me off and picks me up .You wouldn't have to worry about dealing with the car seats either as you will have enough to worry about flying with two small children. I wish you the best of luck!
I hate to admit it, but you will get the stink eye from quite a few of the seasoned business travelers who cringe at the sight of small kids or babies in line at the security check point or for their flight. I'll admit that I'm guilty of this too, having spent my fair share of time trapped in the air with screaming babies and chair back kicking and curious toddlers.