I missed the part about you looking for a design that would be used as a kids bow that would be the same as shortened adult bow.
The kids bow and the adult bow won't have a similar design as far as width and length goes. Most of my kids bows would be an inch wide with a 3" handle section at the most. Because I use osage, all of my adult bows are 1 1/4" wide and 64" long for up to a 28" draw and have a 4" handle section, I may go to 66" long for a 29" draw and to 68" or more for a 30" draw. I had a number of bows that failed for the guys with a 30"+ draw so I stuck to making bows for the 28" draws and less because I replaced broken bows, it set me back a week or so to replace a bow.
One guy broke two of my bamboo backed osage bows, I made him a replacement for the first broken bow and refunded his money on the second one. I found out later after more broken bamboo backed bows showed up that I had gotten a run of bad bamboo from Frank's, it looked good but wouldn't hold up.
You may find like I did that a kid's bow is the most difficult of any bow to make, when you get down to a bow in the 15# range you don't have hardly any
wood thickness left in the limbs and one too many swipes with your scraper will make the bow hinge, you have to have the tiller spot on to pull it off.
I think you need more reference material to study designs; I made up my own design which performs well for me and the people who own one of my bows. Some designs are fit for white woods, others work well for osage and yew.
Because you are using mystery wood to make your bows, make them wide, flat bellied and long.
People get hung up on trying to gain a few extra feet per second out of their bows, which is good because we all learn a little more from their efforts. I go for smooth drawing, stable and long lasting with very little set.
These bows span my 26 years of bow making before old age and injuries shut me down, the static with a little set has been shot so many times over a ten year period that if I guessed the number of arrows that had been though it would sound like a lie. The top bow is bamboo backed, I had it stored too close to the ceiling in my shop and the summer heat cause the bamboo to crack and the handle to pop loose, I am in the process of adding a new handle to the bow, I had already fixed the minor cracks in the bamboo