We run a business in which we flip houses, so we sell several homes every year (although we are not living in them). My recommendation to you would be to show your house by appointment. It's really not a big deal to most buyers - it's not like most people just happen to be driving by with their agent, and say, "Hey! That place has a sign on the lawn, let's stop there!" No, typically the agent will want to preview the house (meaning they'll come by without their client) and if they feel the home meets the needs of their client, they will then make an appointment to show the home. THE single most important driver is price - if you're at the right price, your home will sell quickly despite the bad market. Make sure your agent has your home listed at the correct price the day you go on the market - dropping the price later makes you look desperate, giving buyers more leverage. Staging your home is necessary, but secondary to price.
When they DO make an appointment, as long as your house is pretty much within an hour of being spotless, you'll be fine. I'd take the litter box, the cat, and the kids out of the home when you know it's being shown (I know this will not make the cat happy, but it is what it is). When we know people will be coming by to view a house we're selling, I'll throw some cookies in the oven so the house smells inviting, and then you have a nice plate of cookies for them to snack on while they tour the house. Also, before you leave before the showing, turn on every light in your house. (Yes, every single one.) The more light, the better. As long as you've removed any clutter and the house is clean, you're good to go!