Let's play Circle of Death

That's where we all sit in a circle and I call out two names. Those two people go in the middle of the circle and get to fight to the death. Got it? If not, then come on over to my house. That's Eli's and Leah's favorite game! They play it all the time. The only bad part is, they are the only two who ever play.

Seriously, Eli and Leah used to be best buddies. Now, all they do is fight from the minute they wake up, literally. The fighting started before 7am today. I can't take it. When they fight, I try to break it up as best as I can, but I'm not a good referee. It's not shouting, just wrestling and bugging each other. You know, poking and kicking and pushing and stupid, annoying, little stuff that builds up to them screaming and crying and hurting each other. I try giving them time-outs and putting them in their rooms. It doesn't seem to help too much. Got any suggestions? Our place is kind of on the small side, so I think part of the problem is there's not too many places for them to go to get away from each other. But they don't exactly want to get away from each other either. I'm at a loss. HELP!!!

What Eli's and Leah's relationship used to be like:

I would post pictures of what their relationship is like now, but I don't want to reinforce the behavior.