I think when you see your kids so infrequently, it can be hard to spend that time nagging them to do not-so-fun things like cleaning up after themselves. I can sympathize with wanting to just spend time having fun and not so much time enforcing rules. Holding onto that perspective might go a long way toward helping you cope with the extra mess when the kids are around.
And here are some ideas, and I'm sure others will be along with other ideas. What works for one family doesn't always work for another, so hopefully you'll get lots of suggestions to pick and choose from.
If you STB-husband is generally on top of keeping the house picked up and clean, I would probably ask him to pitch in for the extra mess when the kids are there. I think I would be understanding that he doesn't want to spend time picking up that he could be spending with the kids, but maybe he can do a quick pick-up while the kids are setting the table for dinner or taking a shower or after they are in bed. If their laundry sorting technique creates extra laundry, ask him to be responsible for some of the extra loads that happen on "kid weekends." It also can help to make sure they are set up for success, like putting a hamper wherever they are getting changed or having a laundry basket for clean clothes next to the hamper for dirty ones.
With our kids (most of whom are younger than your stepkids) we have beenworking this summer on getting the kids to help keep things picked up. First, I've picked a couple things that I am "training" them on (for lack of a better word) and those are the things I spend my energy enforcing. One is taking care of their pool stuff, the other is not leaving clothes and shoes around the house everywhere. So when we get home from the pool, I remind them that they are responsible for getting their towels and shoes out of the car, that their towels and swim suits need to be hung on the line. Then I follow through making sure they did those things. It didn't take long for them to get into the habit of dealing with their pool stuff rather than leaving them in a wet pile on their floor.
The other thing we sometimes do is to have them do a specific pick-up task before something else happens. So if we are about to leave to go to the pool, I ask them first to pick up the front room ( giving each a specific, finite task: "4-yr-old, put the books on the shelf, 6-yr-old find all the cars and put them in the car basket, 8-yr-old please bring all the doll stuff back to the play room"). We try to make it fun (like a race against the parents, or they get to assign the grown-ups' task, or we put on music and do dance party clean-up, or whatever), and we try to give them tasks that they can accomplish fairly quickly. They seem to do a lot better with very specific requests-- sometimes I think "clean up" seems overwhelming and they don't even know where to start.
Good luck! I hope some others have some good ideas-- I'll be following to try to find some new ones for our house, too!