Yeah, I'm sorry, BTDT, this sucks, no two ways about it. You can do it, it just means organization and flexibility, which is of course very hard with littles. My advice:
1. Declutter. Then declutter again. Then declutter again, including pantry, fridge, closets, etc. -- everything has to look more spacious than it really is. We went through like 4 rounds before our realtor said it looked appropriate. And we are not exactly hoarders; literally, I had left one corner of the family room as a designated play area, with a play mat, toy box, and one riding toy, which I thought would show families what a good floor plan it was. But our realtor said even that was too much and we should re-stage that area with a comfy chair and lamp. By round 4, I thought the place looked ridiculously sterile and empty, but the feedback we got improved dramatically, and the place sold within a week of our final decluttering effort.
Side note: we ended up selling to another family with young kids. Apparently, even families with kids want the fantasy that their house will not look like kids live in it.
2. Get out of the house when you have visitors. If you can schedule around naps, great. If not, ask the realtor to always give you at least an hour's notice and drive around if you have to while your kids nap in the car.
3. To facilitate 2, always have a "go" bag by the door with snacks, diapers, toys, books, sunscreen -- anything you might need to be out and about with the kiddos for an hour or two. Replenish the bag first thing when you get home.
4. Pick up while you go. Yes, I know, awesome theory, but in real life it slides. It can't slide when you're trying to sell the house. On the plus side, you will have far, far fewer things to pick up, because you've done such an awesome job on step 1. :-)
YMMV, of course -- if you're in a hot market, you may not need to do all this stuff. Then again, a house is a huge investment, and even in a hot market, wouldn't you rather be selling that one perfect house that everyone wants to buy?