I just went through selling a house with a one and a two year old. I didn't like myself very much during that time, as I was stressed and picky about how the house looked at all times (SOOOOO not me!!). With that said, though, it actually stayed cleaner than I expected it would, and we made it through just fine. Here are the things that helped me:
-I went through and packed up as much stuff as I possibly could before we listed the house. I believe it was on here that I read that someone's agent had told them that they could pack boxes and stack them in the garage. People aren't emotionally attached to garages, so seeing boxes stacked in there is ok. I tried to keep neat stacks, but there was quite a bit out there. All the kid's stuffed animals, a lot of their toys, kitchen stuff that I didn't use all the time, out of season clothes, etc, etc, all got boxed up. The less stuff you have, the less stuff you have to keep clean.
-I tried to do some of the cleaning every day, to keep it up. I had 3 bathrooms, so I cleaned one bathroom every day, and that meant that each got cleaned 2 times a week, but it wasn't overwhealming. I swept and spot mopped daily to keep the floor from getting too bad and needing to be completely mopped.
-I really worked on keeping us in the main living area of the house and out of the bedrooms during the day. This way I could make beds and straighten the bedrooms in the mornings and then not have to deal with them again later if we needed to leave. I knew they were clean.
-Our realtor stipulated in the listing information that we MUST have 2 hours notice before a showing. He told me that I did not have to let in anyone that didn't give notice, and to call him if I had any trouble. I never did. Agents that called were very understanding and worked with me to make sure it was convenient for everyone.
I don't look back at that time with the desire to do it again any time soon, but we made it through just fine, and the rewards of being in our new home are huge.
Hope some of this is helpful to you!!
P.S.- From the other side, as we were also looking at homes at the same time, having some toys out, or in baskets, etc, didn't bother us. The things that we really noticed that turned us off of homes were things like cobwebs in the corners and filthy walls and blinds, etc. We didn't paint our home before selling, but we did wash down all of the walls, blinds, window sills, etc. It made a huge difference in how things looked, with much less effort than complete repainting.