If it were me I'd do the kids' stuff first -- because the kids will be out of the house. I can't purge kid stuff while they're around...Plus, you expect to be fast at it so it shouldn't take forever.

Then I would definitely tackle the papers. I would not plan to finish them. That way you won't be stressed/disappointed when they're not all finished. But for me, the hard part of a major project like that is starting it. Once it's started and I'm over that inertia, I get so motivated to work on it. So if you make a good dent in the papers this weekend, you can probably keep the momentum going by doing a little bit at a time in the evenings or when you have a few free moments (ha! as if those exist!).

And yes, I think you should plan a break for yourself on Saturday too. Do what works for you, but definitely enjoy that kid-free time a little bit too!