I've seen some fairly thin indoor/outdoor carpeting that would work. RV mats may not be long or wide enough in some cases. We have 2 exterior doors and the standard RV mat isn't long enough to fit under both steps and we may get an indoor/outdoor carpet.
A no-shoe rule might work. We remove our shoes and change over to flip-flops when we're going to be in and out of the TT. I made an opening the back of our dinette seat next to the door (about 12x12") to keep flip-flops and shoes in so they aren't all over the floor.
Our long-haired dog is pretty good at tracking in tree needles and dirt and it's a constant job to keep the floor clean. We installed a built-in vacuum cleaner 2 years ago and it's been one of our top upgrades. Gets used a lot, even when the dog isn't with us.
If you have an outdoor shower and can use it to wash dirt off the kids, thick rubber anti-fatigue mats can be used to keep their feet off the ground. We bought one at Lowes that is 36x36" and cut it into 12" squares to make a path to the door. The 12" squares are easier to store too.
