I'm glad other people pointed out what I was going to say. You want to get to security at Midway AT LEAST two hours ahead of time. With TSA regulations, the lines at the airline check-in's, and the fact that you have kids you're traveling with, it's just going to be so much easier if you leave earlier in the morning. I live in Chicago and I only fly out of Midway (I can't stand O'Hare), so I always get there two to three hours before my flight. Sometimes this means getting there at 4am for a 6:30am flight, but I'd rather be early than late (I missed my flight at O'Hare once because of my father).
But yeah, you're going to need time to find a parking spot, to get to the departure terminal, to get to your gate, to go to the bathroom, etc etc etc. It's just easier to plan more time in. Like another poster said, your kids aren't going to be paying attention anyway. My parents pulled my siblings and I out of school once for a trip to the Dells and we hadn't focused on school all day.
Also, depending on where you guys are coming from, you may be able to skip the drive and utilize public transportation. It takes a little longer, but you don't have to worry about paying for long-term parking at Midway. There's a bus system owned and operated by Coach USA called MegaBus where fares start at a buck (seriously, I've taken this up to Milwaukee). The 'terminal' is downtown at Union Station, but it's only a couple blocks to the Orange Line, which will take you right to Midway. Also, another option for depending on where you are is Metra. I take Metra out to Dekalb to visit my best friend pretty regularly (although, technically, it stops in Elburn and she picks me up from there). They have low fares, kids under a certain age ride free, and most of their parking lots have decent rates. It's just an idea, but it might work for you depending on how much luggage you have. If you need any information on MegaBus, Metra, or the CTA (public transit in Chicago), please feel free to PM me, as that's usually how I get around, thanks to being too poor for a car.