What a fun challenge...
Someday things go pretty smoothly and it's great. Other times it's a huge drama. Right now Dominic (14 months old) is into everything, or climbing everything and has also entered that "Mommy hold me all the time" stage and The "Don't EVEN think about trying to go to the bathroom alone" stage. It can make things VERY challenging indeed!
So what to do so you can actually get things done? Lots of people love the activity boxes. I think the idea is great and if they are in a pak n play that might work. For my kid however, if he's out of the pak n play he wants in on what ever we are doing. Sometimes putting him in a highchair next to the big table while we work in the dining room will work, as long as we give him a couple of toys to play with (no crayons yet since he'd only try and eat them anyway!). He pretty much is happy as long as he's in the middle of everything.
If it's a bad day, than it really doesn't matter WHAT we do. He's not going to like it. Those days are hard! Sometimes if I just sit with him and not do anything else for a short time, he'll get happy and decide to go off and investigate some toy or box or whatever has caught his eye and he'll ignore ME for awhile. Other days, it's waiting for that nap so I can do something a little more one on one with the girls. Some times it's bad enough that we just put stuff on hold and take the day off and if we are lucky we can do a little something after dinner while Daddy spends some time with Dominic.
Since we aren't doing a huge sit down type of curriculum most days it's not usually a problem to just change what we are doing. Sometimes it's taking everyone for a walk and just getting out of the house, granted this doesn't work every day especially if the weather is really bad (and in the Pacific NW winters can be wet and miserable!). Maybe pull out a set of toys for a little while and everyone just plays together.
The biggest thing to remember is to try and relax (I often have to remind myself), remember that you don't have to do what you have scheduled for the day..that's one of the beauties of homeschooling! You make the schedule: You can change the schedule.