One solution we have come up with (besides bringing 20 pounds of wet wipes) is to bring along several large pieces of astroturf. This creates a “clean space” where we can unload stuff, sit on to do activities or read, lay down babies, or have the kids put shoes on.
When we pull up to our campsite, the first thing we unload is the astroturf. We unload the camping gear onto one astroturf mat and then have the kids tote all the things they can carry down to a second astroturf mat near the tent site. Later, we use it as a clean space for any non-moving baby we may have. Simply lay the astroturf in the shade with some baby toys, add your baby and VOILA! Just like home! You can also place the astroturf at the opening of your tent so that the kids can sit all the way down to take off shoes or get their hair combed without sitting in the mud. It may seem like a big item to pack, but it is certainly worth the space!