Our class of 2014 has two students with kids (me being one)... It's not impossible, just more difficult. If you have a stay at home wife then you remove a big part of the "problem" equation (how to get kids to school when you both have to be at work or clinicals at 6am).
Otherwise, you just try to balance everything. In fact, I'm in the middle of studying for finals that start next week and go for 8 days or so and had to stop typing to handle my 5 year old. ;-)
You will be tired. You still have to take care of your house, kids, bills, lawn, etc. But you'll live...

I know two guys one who completed Emory, one with 5 kids and one with 4. They said it was difficult at times but definitely doable. The more Established programs (Case Cleveland and Emory) have an easier time placing you closer to home for your out of town clinical rotations but it is still no guarantee. I'm applying this August with 3 so I'm going to remain optimistic.
Good Luck!