I'm going to be watching this thread closely and going back to the other links here so I can get more ideas. I have a two-year-old as well as an infant, so in a few more months we will have two running around here while we are doing school work.
I just want to chime in here that I have been doing something called 'blanket time' with my dd. I got the idea from the Duggars' book but I've heard others speak of it, too. Your child sits on a blanket, with just a couple of different activities, and must stay there and play for a prescribed time. I started with 15 minutes at a time and plan to work up from there. We've done this with our playpen in the past, too. I set the timer and she may get up when it sounds. Eventually I hope to have her sit and play long enough to switch activities a time or two, then have something new planned for her to do......outside with sibling, snack, coloring in her high chair, etc. Right now I'm just training her in how it works. We have had a few times where she cried, wanting to get off the blanket, but I encouraged her to play and reminded her that she needed to stay there until her time was up. She's doing well with it overall. I'm happy with our progress and eagerly anticipating how it will help us while schooling. And I agree that it's great for her, too.
Still, I have had to rethink my definition of peace.

She is a good, happy girl most of the time but it's still very busy around here. We find our peace in the midst of the storm, so to speak.

I do try to keep all of my children from making too much unnecessarily distracting noise, but I am also trying to help them understand that they can learn to focus and tune out the distractions when needed. We all do it in the 'real world' all the time, right? I also have The Toddler's Busy Book and will be taking ideas from there for activities to keep her engaged.
Hope that helps some. I know others will have more suggestions for you, too.
