Kennith, I'm totally not qualified to answer your question, but I can tell you what I did this past year to set up my mini-bog. I'm wondering though, are you going to sink the pool into the ground or leave it on top of the ground? A kid's pool sounds like a neat idea! I got a pool-form from Lowe's at the end of the season that was bolted onto the wall for less than half price. So, my bog came with three bolt holes on the bottom (mine I dug a hole for) and I added 3 more holes a couple of inches down from the top. I was worried about too much water pooling in the bog, but after the ground got saturated (it took about 2 weeks), the water drained off plenty well (I maybe could have filled in one or two of those bottom holes).
I didn't add any perlite to my mix, I used roughly 1 part WET peat (packed) and 1 part coarse sand, maybe a little more peat than sand. I've read since, and would probably do myself, that 2 parts peat to one part sand is good. The extra peat would hold moisture better.
What I didn't know until I started stocking my bog is the different requirements for different types of bog plants. Your plants will make the amount of drainage an issue, some want water all the time (or at least moisture) and some will want periodic "flooding". My terrestrial orchids don't want to be as wet as my pitchers for example.
Hope that's some help. Good luck with the bog!

I was thinking of using spaghnum moss and we have a granite decomposed sand we can get a rock company. What I am also curious about is some websites recommend using 10% aquatic charcoal. Is this really necessary or just one more thing to buy?
Elaine