Peeing during playtime could be just that they're trying to mark everything. They want to make sure everyone knows it's THEIR play area.
We were having problems with one of our bunnies always peeing outside her litterbox. No matter what corner I put it in, there'd be pee on the bottom of the cage - until I realized the problem was just that the litterbox was too small. She could fit in it just fine, but she'd back up a bit and stick her butt up to pee, and it would go OUT of the litterbox. So I switched to one size bigger, and she's been doing great now. Now, it doesn't even matter where the litterbox is - she keeps pushing it around to whatever corner (or even the center of the cage) that she wants it in, and then uses it there. After I clean it up I just put it back in the front of the cage, and she rearranges to to be wherever she wants it.
What I'm using is just a basic plastic cat box from a supermarket. It cost me about $4.50 - which is way less than the pet store ones are, and it works better. I threw the corner litter boxes I had away since they didn't work and they were too small anyway. I put some compressed paper pellets in the bottom and some hay ontop, and it works out great.